Before Slaneesh, all Eldar can serially reincarnate with continuity of identity, just as the Dark Eldar can do after the Fall. It's just easier, as they don't need to use condensed pain to retrieve the soul from Slaneesh, as they're free to move around the war, protected by their gods.
It's made explicit (I think in the Haemunculus Codex) that it would be possible to resurrect Eldanesh himself if you could supply enough pain to pull his soul out of Slaneesh.
The ancient Eldar, like the Dark Eldar, can basically respawn. Their biological bodies can wear out, but they can just get new ones to inhabit, and if they die by violence or misadventure can just wait for someone to grow them a cloned new one.