In the end of the last film Frodo and Bilbo gain Access to Valinor. Are they immortal like the elves when they get there or do they die "normal"?
From Tolkien's letter #325:
As for Frodo or other mortals [who enter Valinor], they could only dwell in Aman for a limited time - whether brief or long. The Valar had neither the power nor the right to confer "immortality" upon them. Their sojorn was a "purgatory", but one of peace and healing and they would eventually pass away (die at their own desire and of free will) to destinations of which the Elves knew nothing.
Also, from letter #154:
I have said nothing about it in this book, but the mythical idea underlying is that for mortals, since their 'kind' cannot be changed for ever, this is strictly only a temporary reward: a healing and redress of suffering. They cannot abide for ever, and though they cannot return to mortal earth, they can and will 'die' - of free will, and leave the world.
So no, they can't be made to live forever, but they could live quite a while.