Immortality

[Arwen Imladris]

I think that with Arwen, she thought that all of the ships that could take her would be gone by the time Aragorn died. If she was immortal she would have to stay in ME the whole time.

Also From Apendix A, after Arwen and Aragorn have been together for a long time, Aragorn is about to die and gives Arwen one last chance to turn back to her elves:

Aragorn: to repent and go to the Havens and bear away into the west the memory of our days....
Arwen: Nay lord, that choice is long over. There is now no ship that would bear me hence, and I must indeed abide the Doom of Men...

Hope that helps