In The Children of Húrin, it is said that Beleg sickened nearly to death when he was starved of food and water for two days. It is said that Maedhros survived for a long time (probably) without food.
What is known about factors that affect the starvation of Elves?
The obvious difference is that Maedhros was from Valinor, while Beleg was a Sindarin elf that had never been to Valinor. There are other references to the hardiness of the recent Noldorin arrivals (all quotes from The Silmarillion):
And [Fingolfin] and his host wandered long in misery, but their valour and endurance grew with hardship; for they were a mighty people, the elder children undying of Eru Ilúvatar, but new-come from the Blessed Realm....
("Of the Flight of the Noldor")
The Noldor, outnumbered and taken unawares, were yet swiftly victorious; for the light of Aman was not yet dimmed in their eyes....
(Regarding the Second Battle, Dagor-nuin-Giliath, in "On the Return of the Noldor")
There Maedhros in time was healed; for the fire of life was hot within him, and his strength was of the ancient world, such as those possessed who were nurtured in Valinor.
(after Fingon rescues Maedhros, "On the Return of the Noldor")
However, it still seems strange that Beleg would still become so weakened after only two days, given other references to his hardiness and the fact that even we frail humans can go two days without food (if not necessarily water) without nearly dying. The Children of Hurin stems from some of the earlier stories, and may reflect a conception of the Elves that changed in later versions of the mythology.
