[Belegorn]

Howdy,

Early on for Elves, in their infancy in ME, it is said that:

"in their early days death came more readily; for their bodies were less different from the bodies of men, and the command of their spirits over their bodies less complete. This command was, nevertheless, at all times greater than it has ever been among Men...Their fëar...far excelled the spirits of Men in power over that 'raiment', even from the first days protecting their bodies from many ills and assaults (such as disease) , and healing them swiftly of injuries, so that they recovered from wounds that would have proved fatal to Men." [MR, pp. 218-219]

So really it has to do with the destiny of their spirits as well as the eventual change in the bodies of the Elves which were early on similar to that of Men. I think as time goes on the body is consumed and becomes deathless, almost like the inhabiting spirit, for the Elves.