[Amezarak]

Elves "fade" because they live so long their spirits gradually "wear out" their bodies due to the fallen nature of the material world (thanks to Morgoth), which the power of the Valar can repair - the Valar also literally reincarnate them when they die, because Elves are not supposed to be without bodies in Valinor period (unless they've been bad.) They are quite capable of living for many, many thousands of years without any "source of magic".

I think RoP introduced this idea, but it is not in Tolkien.