For my story, I need South African apartheid to still be alive in the 1990's. Everything else is more or less the same. For example, the Eastern block still collapses in 1989.
What would be the minimal changes needed to prevent apartheid collapse in the beginning of the 90's?
Oddly enough getting rid of Mandela as we know him probably would be enough. Getting rid of de Klerk would probably be enough, as well.
The problem with apartheid was not downright collapse, but simply that it had no future. As such it was perfectly rational for de Klerk to think that it was not a question of whether apartheid should end, but when and how that should be done. I think that was common opinion in South Africa at the time?
Anyway, the timing would depend on the best time to negotiate. In general that would be as soon as possible since things will only get worse, but given the the perfectly justified distrust on both sides, the actual best time would be "when both sides have leaders able to ignore the distrust".
That pretty much means de Klerk and Mandela. Neither of them had a clean reputation on the other side, it would have been easy to insist on negotiating with someone "clean". For example, in both Syria and Iraq the US had strong opinions about who they deem acceptable. In both cases the results have been fairly disastrous. In South Africa this would have made any negotiated end to apartheid impossible and easily delayed the end by a decade or more. People can be fairly stubborn if they have no real choice.
A related issue is that while personal trust or approval was not necessary, it was necessary to be able to trust that the new government will at least try to avoid open retribution against the whites for the injustices of apartheid. Mandela is pretty much the only person who could promise that and have a realistic chance of keeping the promise. I do not think de Klerk would have been able to take the risk, if Mandela had not been available.
If you want minimal the easiest is probably to replace de Klerk. He is not nearly as iconic as Mandela. People outside South Africa might not even realise he was missing. You can also just tweak de Klerk slightly, either by him not realizing the time is running out on apartheid or by making him more law and order type and refusing to negotiate with a terrorist.
Oh and I am far from being knowledgeable about South African politics, so take the advice above with a grain of salt. It is basically my impression of the general pattern of things as seen from far outside.
Empire.
this was fun to think about but I am not sure it qualifies as minimal. That said these events would probably not greatly affect the world outside Africa. An Israeli / S. African nuclear test really did happen, although not in a military context.
from http://www.timemaps.com/store/timemaps/2012/4/africa_ad1960.jpg
• 1939. On the outbreak of world war 2, Afrikaaner pro-German influences prevail and South Africa remains neutral in the war, skewing South Africa permanently away from British and towards Afrikaaner influence in domestic politics. This leads to an influx of German refugees during and after the war. Among the refugees are ethnic Germans who have ideological differences with the Nazis. Paradoxically, large numbers of German Jews also emigrate – these correctly perceive a welcoming environment among the Afrikaaners. http://www.sahistory.org.za/article/afrikaner-jewry-south-africa These immigrants augment and fortify the white ruling class, improving its administrative efficacy along German lines without the Nazi cruelty and jingoism.
• In the mid 1960s the crumbling white supremacist government of Rhodesia cedes the state in its entirety to South Africa, fearing (correctly) that the white minority will be disenfranchised and driven out if joint rule with the black majority comes to pass. This move is facilitated by the large number of British-descent South Africans who relocated to Rhodesia during WW2.
• Shortly thereafter, joint Rhodesian / South African troops occupy Mozambique and then Angola, putatively to restore order as the Portuguese government withdraws. This they do well, and these former Portuguese colonies are incorporated as South African protectorates.
• Over the late 1960s and early 1970s, white populations of newly independent African nations and especially Congo flee to the enlarging South Africa, bringing with them their wealth but also an interest in retaining African financial and commercial ties – or retaking their old homelands entirely.
• In 1976 South Africa (with Israeli assistance) drops a nuclear weapon on Angolan communist insurgents (and a large number of unacknowledged Cuban “advisors”). The USSR and US protest but cannot join forces to take action and neither can act unilaterally. This show of strength by SA ends the insurgency in Angola and also raises the esteem among Africans for South Africa as a domestic superpower. This, together with the earned reputation for incorruptibility among South African administrators, leads to the success of a South African backed insurgency in Congo / Zaire and the addition of this nation to the South African polity.
By 1990 successful oil exploration efforts in Mozambique and Rhodesia have moved South Africa to the third biggest oil producer in the world and it is the chief political influence in subsaharan Africa. Despite the continuation of Apartheid policies, most of the citizenry deems this form of fascism an acceptable price to pay for noncorrupt government, peace and prosperity.
One of the things that caused the final breakdown of the apartheid system was the big international companies pulling out as the boycotts started to bite. Barclays was one of the last, though the boycott campaign took 16 years eventually they pulled out in 1986, and with the loss of the big banks cutting off the governments access to finance it was just a matter of time.
There will be a lot of talk of Mandela on a subject like this, but he could just have been kept in prison. He was known about but not known until his release, and he was effectively released to be someone to negotiate with to manage the transition.
As with any political system it's propped up by the financial stability of the country, the loss of finance is the fall of the government. FW de Klerk wanted to change the system, Thatcher was propping him up to help manage a stable transition. Removing Thatcher could have caused de Klerk to fall and lead to either an unstable transition or delayed transition, removing de Klerk could have delayed the transition but you'd still need a line of credit for the government to operate.
(Except that I like Will answer, but I'm not sure it counts a minimum change)
Earlier Rwanda genocide (or additional Rwanda style genocide nearby), that would convince the West to drop serious sanctions because stable regime is still a better choice.
Earlier Robert Mugabe economic success in printing money in nearby Zimbabwe (to make enough Blacks reconsider whether ending White rule would really make them better off...).
Deadlock of peace negotiations (or a minor blood bath). In real life Nelson Mandela just after release from prison was speaking about implementing quite a few communist policies and until his last days was calling Muammar Gaddafi as great friend. In your timeline I see a great potential for Mandela to be a bit more idealistic, be released and deported as part of some West brokered sanction lift, and end up his life peacefully on political exile, loved by radical left and treated as an embarrassment by the rest.
Huge oil reserves findings in South Africa. The Oil Embargo was very powerful instrument to put pressure on the apartheid regime after the fall of the Shah. West hated apartheid but they hated USSR even more. The soviets were main beneficiary of high oil prices after Yom Kippur war and the fall of the shah.
Considering Gulf states complete disregard for human rights even today, not to mention all the countries that sold weapons to Saddam (even nuclear reactor) when he was gassing civilians every day, its not a big stretch to believe that the apartheid would have been safe if they had oil, especially in large quantities to export in order to tip the balance against Gulf states and the USSR.
http://richardknight.homestead.com/files/oilembargo.htm
http://kora.matrix.msu.edu/files/50/304/32-130-1C09-84-Embargo_Apartheids_Oil_Secrets_Revealed%20opt.pdf
This probably would not be done, but improving the economic conditions for blacks would probably have allowed apartheid to survive longer.
Most people want a quiet life. Even very poor people who have minimal political and civil rights generally just want a quiet life.
But they also want some hope, some reason to believe that their conditions will slowly improve. Slowly opening up more avenues for blacks to live better lives would have made a huge difference.
Expecting any population to exist as a service class to maintain the comfort of another while they wallow in poverty is simply asking for a revolution. Usually gets one too.
So simply improve the conditions. You'd be surprised how little you have to improve things to get away with it.
Fundamentally it's a system that would fail. You cannot suppress the majority of your people and expect that to do anything but lead to revolt. It has never worked anywhere.
You are apparently not trying to save apartheid, just prop it up for an extra decade.
A few turning points might be enough:
A previous answer cited de Klerk and Mandela as the right people in the right positions at the right time to find a peaceful solution. de Klerk, in particular, would not be hard to handwave away, then the negotiations fail.
throw a few bones to the protesters in Soweto in 1976 to quell the riots.
unite blacks and whites in a war against a common enemy
do something to neutralize Stephen Biko (spike his scholarship? Toss him in jail with his brother in 1964?)
go back even further and slow down the Civil Rights movement in the US. A US still dealing with hard civil rights problems will be less likely to pressure South Africa.
The smallest change that could reasonably allow apartheid to exist in South Africa would be to, instead of eliminating apartheid altogether, replace it with a system in which citizenship and the right to vote is based not on race, but on wealth. This could be proposed as a way to ensure that the country is governed by only the most intelligent members of society in order to combat populism and maintain the most effective government. One simple way of accomplishing this is by restricting the vote only to landowners, or to landowners who control more than a threshold amount of property. Theoretically, anyone could become a voting citizen by purchasing land, but in a country where the vast majority of land is controlled by wealth white landowners, the effect would be an apartheid government.
While this wouldn't be a de jure system of racial apartheid, the effect would be to disenfranchise the largely poor black portions of South African society. The exclusion of some poor whites and inclusion of some rich blacks would give the government the ability to say that it's not a racist apartheid state, while having a voting citizenry comprised almost entirely of white voters. While removing the apartheid state may have been inevitable in the modern world, removing it and replacing it with a system built on entrenching the racial power hierarchy created by the apartheid state would be similar to what's happened in many other countries.
This is, for example. almost the exact thing that's happened in many schools in the American South, post-desegregation. While there is no law creating separate schools for white and black children, wealthier white students in many areas attend private schools that are almost entirely white. Schools aren't segregated by law, but since one effect of segregation and racist policy was to create race-based economic stratification, the effect is the same. Schools are segregated on an economic basis, which means that there is a de facto racial segregation of schools. The same could be applied to government.
So far the importance of Mandela and de Klerk has been emphasised, and while this is fair I think it's important to add context by pointing out the historical pressures on the apartheid regime. I am aware you want as little historical disruption as possible, but that will depend on what factors you view as most pivotal to the end of apartheid.
Firstly, one of the most important moments in South African history is the Sharpeville Massacre in 1960. Without it the international community would likely take longer to be mobilised against apartheid. And perhaps more importantly, internal stability would be greater, dissent less.
After this there were two major events which contributed greatly for and against apartheid. Firstly, the start of the South African Border War in 1966, and thereafter the creation of the Krugerrand in 1967.
The Border War lasted until 1990, and was an extremely challenging conflict. In 1988 around 71,000 South African soldiers were deployed as far away as Angola. The cost was offset by sales of Krugerrand; a gold-copper alloy coin minted in South Africa which became economically essential for the regime, and has since saturated global gold markets. In 1984 half of South Africa's foreign exchange income was from Krugerrand sales alone, with $600m USD worth marketed that year in the US. That was, until Reagan banned their import in 1985. Additionally, the Cubans were instrumental in that conflict, deploying up to 20,000 soldiers in Angola.
So what you can do to reduce stress on the regime is negating a few important pressures. Firstly, as stated, Mandela and de Klerk didn't exist. Secondly, the Sharpeville massacre didn't happen. Thirdly, the Border War did not happen or had its scope and duration limited. Perhaps the Cubans never got involved. Fourthly, the price of gold was higher or simply there were never import bans on Krugerrand until much later.
Perhaps some relatively subtle changes to all of the aforementioned could in sum have a profound impact on apartheid's longevity.
There is a very simple scenario to fulfil your criteria.
FW De Klerk's predecessor was PW Botha. He was a both a hardliner and a strong man that would resort to military power when it suited him. In February 1989 he had a stroke which weakened his political power to such a degree that the 'reformist' FW De Klerk and Pik Botha was able to oust him from power.
It is unlikely that PW Botha would have been willing to release Mandela and un-ban the ANC as done by FW. Even though sanctions were starting to affect the South African economy, the army was still powerful and able to prop up the government and suppress the growing resistance inside South Africa's 'townships' for a number of years. Probably to at least the end of the 1990's.
So I would say the PW's stroke triggered a profound change to the South African political landscape.
Interesting question and interesting answers as well. Allow me to throw in my 2 cents as I’ve actually pondered the very same question.
The coloured and Asian populations which irl were allowed limited participation in the country’s politics via the tricameral parliament must be fully enfranchised. So, instead of a tricameral parliament being created in 1984, coloureds and Asians are given full citizenship rights. This isn’t too fanciful as these two communities were seen as being more amicable towards the apartheid system and coloureds even partly shared European ancestry with the whites. Besides, the white government was most afraid of the blacks, evidenced by the term Zwaart Gevaar, i.e. Black Threat. So, giving equal rights to the coloureds and Asians would likely be seen as a necessary sacrifice to gain some much needed support against the blacks.
The Bantustans or Homelands need to be turned into actual states. If you look at the map of these territories you see that they are completely unworkable as independent states, which is what the South African government tried to present them as. 
Increasing their territory and making them actually contiguous would not only make them look as true states, and not just reservations for blacks, but would give the individual black ethnic groups more space to occupy. Perhaps it could look something like this 
Furthermore, arguably most importantly, South Africa would have to comply with the numerous resolutions of the UN and renege their control of South West Africa, aka Namibia. The continued occupation of the territory was indeed one of the biggest reasons for the ostricism of South Africa from the international community, perhaps as big as the apartheid system itself. With Namibia being granted independence and, consequently, the SADF withdrawing from Angola, Raegan and Thatcher’s policy of “constructive engagement” would be hailed as a success and a viable alternative to sanctions and disinvestment. As for the coloured and white populations of Namibia, many of whom spoke Afrikaans, those could be granted a right of return and government assistance in moving to South Africa proper thus augmenting the numbers of the non-blacks.
Lastly, and in connection with the second point, the Homelands would have to be given full independence both de jure and de facto. The black population would have to be confined fully to the homelands and allowed into South Africa itself only in very limited numbers and as a temporary laborers.
I believe that if the apartheid regime of South Africa could have ever had a shot at surviving it would have been by taking the steps that I have described above.
If you rig/change the 1992 yes/no referendum you could effectively stop the government from continuing the reforms /negotiations that allowed for the end of apartheid amd the new constitution.
A few lost votes here, a few added votes there. Mark a few ballots as invalid, knock a few people off the registeration polls. Play the media to heighten tensions as well as make people think their votes aren't really needed. It doesn't even have to be a large percentage gap, just 3.8 % would be enough.
The right wing criticised the referendum and accused the government of electoral fraud. They had lost where they had been the strongest, in the Afrikaner heartland and in the big cities. Treurnicht claimed that media propaganda, foreign intervention, threats by businesspeople against employees and electoral fraud had resulted in a "Yes" vote. However no evidence has yet been put forward regarding electoral irregularities.
Now I don't know of this would be enough for a long term change but it will definitely give the Nats the 'backing of the people' and the political mandate to continue as before for the next few years, regardless of what the rest of the country's inhabitants want.
One of the main reasons for instituting Apartheid was the untrustworthiness and violence of the Zulu settlers.
When they invaded South Africa they occupied it by simply slaughtering all the existing inhabitants (black or white). Attempts by the Boer farmers to negotiate peace were used by the Zulu as an effective means of gathering Boer leaders for signing treaties in order to kill them. E.g. Piet Retief Delegation Massacre.
The Zulu culture made social coexistence impossible.
The only practical solution for a lasting peace was for the militarily superior Boers (and later British) to set up a system that would physically separate the Zulus from the rest of the South African settlers. That system became known as apartheid.
Today, we can see the effects of the removal of apartheid. Being a white farmer is now the most dangerous profession in South Africa. E.g. South Africa's Most Dangerous Profession. (Don't read this article unless you have a strong stomach for brutal violence.)
For your purposes, perhaps you could have apartheid's being relaxed earlier than it was, and have some extremely violent events occur as a result (e.g. as in the Farmer article, but more concentrated in time and location). This would demonstrate, both to the South African government and the world at large, that Apartheid is still necessary.
