Immortality and the sons of Elrond

[Inziladun]

The end of (Elrond's) sons, Elladan and Elrohir, is not told: they delay their choice, and remain for a while.

Letters # 153

That's what the Professor had to say about it. It would seem that after the departure of Elrond Elladan and Elrohir didn't figure much in the later histories. That would have been in keeping with the accelerating decline of the Elves in influence and importance.