[Raynor]

Originally Posted by Lord Sayan

I basically think that the undying lands had SOME charm or power for otherwise why would Frodo say to sam-"...my wounds are too great to be healed in Middle Earth Sam.."(or something like that) perhaps old wounds could be forgotten perhaps life could be extended indefinitely i think old JRRT himself wasn't clear on this he has contradicted himself many times.

Tolkien addressed this quite on point:

Originally Posted by Letter #153

Immortality and Mortality being the special gifts of God to the Eruhini (in whose conception and creation the Valar had no part at all) it must be assumed that no alteration of their fundamental kind could be effected by the Valar even in one case: the cases of Luthien (and Tuor) and the position of their descendants was a direct act of God.

Originally Posted by Letter #325

As for Frodo or other mortals, 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 sojourn 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.

Originally Posted by Aman and Mortal Men, Myths Transformed, HoME X

The Valar were not only by Eru forbidden the attempt, they could not (emphasis original) alter the nature, or 'doom' of Eru, of any of the Children, in which was included the speed of their growth (relative to the whole life of Arda) and the length of their life-span. Even the Eldar in that respect remained unchanged.