[Galin]

Originally Posted by Ibrîniðilpathânezel

(...) At the moment, I don't remember precisely where he said it (I believe it was either in the Letters or in the HoME books), but it was believed that because of the presence of the Powers, a mortal in Aman would wither and die even more quickly, like a moth near a flame. (...)

I don't think they would die more quickly, as JRRT seems to expand upon this in Myths Transformed. From Tolkien's essay Aman (and Aman and Mortal Men) published in Morgoth's Ring:

'If it is thus in Aman, or was ere the Change of the World, and therein the Eldar had health and lasting joy, what shall we say of Men? No Man has ever set foot in Aman, or at least none has ever returned thence; for the Valar forbade it. Why so? To the Númenóreans they said they did so because Eru had forbidden them to admit Men to the Blessed Realm; and they declared also that Men would not there be blessed (as they imagined) but accursed, and would 'wither even as a moth in a flame too bright.'

'Beyond these words we can but go in guess. Yet we may consider the matter so. The Valar were not only by Eru forbidden the attempt, they could not 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. Let us suppose then that the Valar had also admitted to Aman some of the Atani, and (so that we may consider a whole life of a Man in such a state) that 'mortal' children were there born, as were children of the Eldar. Then, even though in Aman, a mortal child would still grow to maturity in some twenty years of the Sun, and the natural span of its life, the period of cohesion of hroa and fea, would be no more than, say, 100 years. Not much more, even though (...)

'But in Aman such a creature would be a fleeting thing, the most swift passing of all beasts. For his whole life would last little more than one half-year, and while other living creatures would seem to him hardly to change, but to remain steadfast in life and joy...' JRRT, Aman and Mortal Men

As I read this, the 'guess' would seem to indicate that Mortals do not actually age more swiftly, but that they would seem to wither more quickly, by comparison to the world around them.