This is touched on a bit in the GURPS Transhuman Space RPG setting. Economically, more and more of the world's wealth is locked up in the hands of the first immortals, since wealth tends to beget more wealth. Also, an ageless workforce (plus automation) means more and more of the younger generations not only don't have jobs, but will likely never have jobs. This results in various social problems of greater or lesser degree, depending on the society in question.
Wouldn't that just cause a revolution or emergence of socialist system? Or even deliberately Luddite society?
I think that falls under "depending on the society in question." A socialist economy might actually have less trouble coping with the weirdness of the situation. Depending on the numbers of those younger generations, though, they could either be a marginalized minority or a vast, discontent majority. In the former case they're screwed; in the latter case they'll ultimately remake the system by weight of numbers unless you assume that the system is a perfect tyranny.
(1984 is a 'perfect' tyranny, for example, or at least Orwell portrayed it as one. Perfect tyrannies are the ones that can't be overthrown even in theory, except by Alien Space Bats coming in from outside the system. In real life, there arguably aren't any and hopefully can't be any).
Then again, socialism as we traditionally understand it might have trouble with this situation too. When you think about it, changing something about human nature as basic as "whether people die" should make a lot
of human philosophy and political theory obsolete, so no surprises there.
I don't really think that any society can keep up an indefinite status quo that looks like:
1) Many people have no work
2) The people who do have work must work very hard to keep their job
3) You must work to live, or work to avoid misery.
This seems to me like it's going to be unstable by default- because almost every person in the system would be better off if the work were redistributed. The system may last a while, because there are plenty of other forces in play, but I doubt it could last for centuries. A system only persists when it makes most people in it feel like they're better off keeping it than they are changing it.