Silmarillion - Chapter 06 - Of Feanor and the Unchaining of Melkor

[Legolas]

Weariness is a way of saying it, but specifically 'grief' is what elves are susceptible to.

Miriel died of grief. A few others may die of grief as well, but no sense in spoiling the story if you're just that far!

The Silmarillion describes it as below in the first chapter, though there's a lot of information there so it was probably easy to miss on the first reading.

For the Elves die not till tile world dies, unless they are slain or waste in grief (and to both these seeming deaths they are subject); neither does age subdue their strength, unless one grow weary of ten thousand centuries; and dying they are gathered to the halls of Mandos in Valinor, whence they may in time return.