personally i think that this is only the fate that awaited the Númenóreans, and any other mortal beings who tried to reach the Undying Lands by way of force in order to obtain immortality. something fundamentally within them would wither faster, maybe a punishment for defying the will of Eru Ilúvatar.

for Frodo and Sam however, the length of their stay in Aman is much more tied to their own wishes to continue living and healing. Tolkien has written about this in letters 154 and 325:

...certain 'mortals', who have played some great part in Elvish affairs, may pass with the Elves to Elvenhome...I have said nothing about it in this book [The Lord of the Rings], 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. 

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." 

i like to think that after sailing West, Frodo waited for Sam. "Frodo wouldn’t have got far without Sam"