There are several factors that caused the Soviet Union to collapse. For now, I can only write about two. Preventing either one of them may have allowed the USSR to survive into today.
1. Soviet Paranoia
Some will say that this is cultural (I do not care to categorize it), but it is probably the most significant factor explaining why the Soviet Union collapsed. There was a great deal of internal paranoia--ie, a fear stemming from Kremlin members, high officials, intelligence personnel, or military figures just ending up missing or disappearing. This was so controversial, that there was a method of detecting whether or not an official was still around, and it involved ballet performances: If someone was supposed to watch the ballet but was not photographed at the event, it was generally assumed that they were silently executed.
But this problem extended beyond internal paranoia, one of the biggest mistakes the Soviets made before their fall was a propaganda campaign to discredit the leadership of a communist faction in Afghanistan. That faction was known as the "Khalqists" and was headed by Hafizullah Amin--and unlike the other communists, they advocated immediate reforms to take the whole of Afghanistan from a traditional society into a secular, even atheist, and communist one. However, those reforms were met by a backlash from the conservative/traditional segments of Afghan society, which caused chaos. In order to distance themselves, the Soviets unleashed a propaganda campaign to discredit the Khalqists and frame Amin as a secret CIA agent, bent on sabotaging communism in Kabul. The aim was to convince the Afghans that the Khalqists were not true communists, so that other, more moderate communist factions can appear more palatable to all segments of Afghan society.
The problem? The Soviets began to believe their own lies. Amin was treated as a CIA agent by the Soviet press, and numerous Soviet attempts to assassinate him failed. So, an opinion that "someone" must be helping Amin began to formulate--naturally, it was assumed to be the Americans. Moreover, the Khalqists, fearing that their time had come, began to make all sorts of political mistakes, overreacting to protests and committing crimes that began to alienate even the left-wing segments of Afghan society. The Soviets felt they had to act fast to preserve communism in Kabul--or else, a government favorable to Washington might be created in Afghanistan. The result? The Soviets invaded Afghanistan in panic, unprepared and without a clear objective.
Today, in many political science classes, this scenario is studied to show the problems of "blowback"--which occurs when actors inject statements that may be false in order to discredit opponents or alter the opinion of certain populations. Sometimes, those statements come back seeming more real than their author(s) ever intended, and that can cause great panic--even amongst well-calculated Soviet intelligence agents. The Soviet invasion of Afghanistan is considered by many to be its downfall, or at least, the beginning of its downfall.
Still want the USSR around? Build a time machine, tell them Amin was probably just politically stupid, convince them not to panic and invade Afghanistan, and that if they do invade Afghanistan on the day that they ultimately did, that Zbignew Brzezinski predicted it at least a week ago--and that the CIA is hellbent on getting revenge for what the Soviets did in Vietnam.
2. The Cold War and American Covert Action
Nowadays, no one denies the lengthy covert war between Washington and Moscow. During the Korean War, Russian pilots flew in Korean-marked jets, and even though the Soviets were not one of the primary belligerents in that war, the top ace fighter pilot was a Russian. Later, the Soviets aided the Vietcong during the Vietnam war. This was supposed to be secret, because when interviewed their officials would say, "What? I have no idea what you're talking about."--plausible deniability.
But Washington also had a hand in clandestine activities against Moscow. The biggest and most famous one was Afghanistan, however, the real success of American influence was not only arming and training organizations to fight the Soviets, it was to convince numerous populations that the Soviets were "evil, Godless commies", while at the same time, the U.S. had a program to show American movies to foreign audiences, and Disneyland was so big, that imprisoned Eastern European dissidents occupied by the USSR or under communist rule, would look outside their jail-cell windows and say "Disneyland"--associating Disneyland with freedom.
As a result, many countries that were supposed to be behind the "iron curtain", were actually behind a very fragile glass wall--with resistance fighters within them (or at least political movements) that opposed the USSR. So, while the U.S. could count on the other four members of the "Five Eyes"--United Kingdom, Canada, Australia, and New Zealand, and often even count on other NATO countries, the USSR had a dwindling number of allies--even outright communist countries, like China and Tito's Yugoslavia, at times during the Cold War, were on the side of Washington.
Furthermore, the Arabian Peninsula and Saudi Arabia were squarely in the hands of American and British oil companies, and up until 1979, even Iran was an American ally and used to contain the USSR, which effectively meant the entire oil of the Middle East was in the hands of Washington and NATO.
Political scientists call this "balancing"--Washington did it much better than the Soviets, arguably because the U.S. was in a much better position after WW2 than the USSR, and so could offer more to its allies, but also because American covert action was based in compellence to force certain outcomes: Latin American countries have socialistic leaders like Allende in Chile, who may favor Moscow? Devastate their economy, rouse their public, then overthrow the regime in favor of a dictator who is more favorable to Washington--like Pinochet. As a result, governments across the world, but especially in Latin America and the Middle East, were under unshakable political instability (economic sabotage, regime change, civil war, etc) because of these covert action operations.
Still want the Soviet Union around? Use that same time machine to tell them to preserve their spheres of influence, so that they do not fall like a column of dominoes. That way, at a minimum, the USSR can avoid being contained (and more or less isolated) from the rest of the world.
Also, tell them that American realists and pragmatists do not see the Cold War as solely a war of ideology, but a war based in geopolitics. Sure enough, the Soviets were not all idealists either, which meant the fact that the U.S. and the USSR were the two most powerful countries, is sufficient for some of their countrymen to be distrustful of the other--or at the very least, very cautious of the other, and for some, like George Kennan, that is enough reason to want to put pressure on the other. Kennan's containment policies combined with the Marshall Plan and covert action worked to turn the world in America's favor.