[Riftmaker]

That isn't entirely true either. After the One Ring's destruction, the power of the elves also faded, and their magical abilities to have enormously long lives waned. There's even a quote of Galadriel saying that her power was waning, and it was becoming more and more difficult to keep the orcs out of her woods.

Also, the fact that Arwen becomes human when she chooses to remain and not return to Valinor is evidence of this as well.

Thus, elves are not 'immortal' in the sense that Maia are, but they do live for a long, long time.