Well... it's weird.
I'm far behind on my Silmarillion lore, but I do know that Luthien, a pure-blooded Elf, required the permission of the Valar to save Beren and give up her immortality.
Arwen is a Half-Elf, and as such is presented with the same choice as Elrond and Elros. She chose the doom/gift of Men in order to remain with Aragorn. She also, in some sort of gesture that must have been more than symbolic, gave her place in Aman to Frodo (and presumably by extention to the other two Ring-bearers). How Gimli was allowed to go is something of a mystery.
In all the cases that exist, Elves give up immortality through some sort of choice presented by the Lords (and Ladies! ) of the West. There is no case in which a pure Elf gives up their immortality for no particular reason. However, as the doom of Men is called by the Elves "Iluvatar's Gift," it might possibly be assumed that some enterprising Elf might have wanted to cut their bonds to Arda. But we don't know of this ever happening.... personally, I'm lead to beleive that a "voluntary mortality" is only possible with good reason, and probably would not be normally granted by the Valar.
If someone more knowledgable has something to add....