How can immortal kingdoms retain their power base over the course of millennia?

Question

The world is divided up into seven continents, each ruled by a family or clan of immortals. Altogether, these immortals number 10,000. They cannot be killed by any means, having the ability to regenerate from any damage completely. However, they possess no other abilities, being just as normal as any human. These immortals rule over mortals, which number in the tens of billions. As the members of the families cannot die, wars between nations are conducted very differently in this world. The families use mortals in proxy wars against each other, pitting their mortals against each other in gladiatorial games.

These games are fought against nations for prestige and bragging rights as a way for immortals to compete. The games are conducted each year, where teams of mortals from one nation participate in contests against mortals from other nations, similar to the Olympics. The teams are supported and funded by the ruling clans. These contests are often deadly, and death is very common, resulting in numerous fatalities every year. At certain special events, the games are meant to simulate actual battles, where groups of mortals go to war with others in a designated, controlled environments with the specific intent to kill the other side.

These contests satiate the immortal bloodlust and desire to compete for superiority with each other. However, it is very obvious that the families are using mortals as pawns in their proxy wars for their own entertainment. This would cause discontent among the masses, which greatly outnumber their rulers. While the family members are truly immortal, they are just like any other human physically. It isn't a stretch to say that an enterprising mortal with desires of grandeur can organize a rebellion and take power from the immortals, imprisoning or otherwise incapacitating them. In addition, their mortal subjects may simply tire of being pitted against each other in pointless wars, risking their lives for those who have the benefit of living forever for their own amusement. They could easily rise up against their oppressors and organize states which are ruled by mortals themselves. In our world, kingdoms are often overthrown by one of those things happening, and most only last a few hundred years at best.

As you can see, the immortal empires are very vulnerable, and their rule can easily be done away with. The families need a way to preserve their rulership over the course of millennia, managing to stay in power while being grossly outnumbered. How can the immortals maintain their power base in a way traditional kingdoms cannot?

Answer 1

It is seen as an honour.

The public narrative sounds like this:

In the past before the reign of the immortals, the various nations were constantly at war with each other. The loss of life was great and senseless. The immortals were the first ones to realize the endless wars were not the doings of humans -- who don't really want to slaughter and be slaughtered by each other after all -- but they were caused by their distant relative the Blood God, who wants to see carnage and martial prowess. Their solution was simple:

Give him what he wants.

The gladiatorial fights provide quality over quantity of carnage. This is what the Blood God really wants, and ensures there are no wars at a much smaller cost of life. The gladiators see it as an honour to participate as it marks them as the most skilled in combat, and their deaths are for the greater good.

However

Since the Immortals are related to the blood god, they also enjoy the bloodshed. As you say, it is very obvious that the families are using mortals as pawns in their proxy wars for their own entertainment. To counter this the public narrative has two more parts

(a) The above is framed as a virtue rather than a sin. The immortals are going against their nature by only having one gladiatorial games for year, while in reality they would prefer to have one every day of the year! What an admirable show of temperance and self-control that we should all strive to emulate!

(b) It doesn't really matter if the Immortals enjoy the games more than we would like. The important part is they happen.

For a modern example, imagine a morally-bankrupt politician who's only concern is to remain in power, rather than serve the people. If they live in a democracy, they want to keep a good reputation with the people, as this means more votes next term. So they make some efforts to keep the people happy. The outcome is that some good gets done even if it is for the wrong reasons. The Immortals are seen like this -- morally bankrupt but in a way that aligns their goals with our own.

Answer 2

The rules for rulers are the same, regardless of mortality

In-depth video answer

In case the link ever goes dead:

It doesn't matter if the rulers are immortal or not, as long as they retain their supporters (the keys to their power) they can remain in power indefinitely.

The only upside of immortals over the mortals is that they can indefinitely improve and learn from their mistakes, unlike mortals who have to repeat that cycle from scratch whenever the previous ruler gets inconvenienced by dying...

Answer 3

Bread and circuses

Voluntary human sacrifice has been a part of stable historical societies. And provided that few people see any real benefit to changing the status-quo, the immortals can openly send dissenters to compete in the "games". It's also possible for them to compete personally against the "winners" in an exhibition match to open the games next year.

As long as everyone is fed and entertained, stability is easy enough. You've eliminated the problem of setting it up in the first place, too. Setting themselves up as demigods allows them to blame higher authority for failures and bask in successes - which is important if there's an outbreak of disease. (They are more likely to condone mass slaughter as a means of disease-control; and perhaps carry it out personally.)

Accumulating skill and knowledge

Any given immortal will have learned some skill to superhuman levels, by being able to practice (much) longer and harder. This can have interesting effects later.

Answer 4

Immortal assassins

Not all of the immortals are rulers, some are not content to watch violence from on far and prefer to inflict it themselves. These immortals hide their identity's and travel often so finding them all is practically impossible.

Mortal rebellions happen from time to time but the result is always the same. The new rulers suffer painful deaths and any captured immortals are released. These assassins are extra deadly because they can use techniques not possible for mortals. Poison tons of food and then eat some before offering it to others, spread plagues, starting fires, suicide bombers that survive the attempt, etc.