"In U.S. Military Arctic Light Infantry Training (ALIT), it is taught that rabbit takes more vitamins to digest than it returns. It is recommended in survival situations to refrain from eating at all if rabbit is the only thing to eat.
The Arctic explorer Vilhjalmur Stefansson, who experienced rabbit starvation himself, wrote:
'The groups that depend on the blubber animals are the most fortunate in the hunting way of life, for they never suffer from fat-hunger. This trouble is worst, so far as North America is concerned, among those forest Indians who depend at times on rabbits, the leanest animal in the North, and who develop the extreme fat-hunger known as rabbit-starvation. Rabbit eaters, if they have no fat from another source—beaver, moose, fish—will develop diarrhea in about a week, with headache, lassitude and vague discomfort. If there are enough rabbits, the people eat till their stomachs are distended; but no matter how much they eat they feel unsatisfied. Some think a man will die sooner if he eats continually of fat-free meat than if he eats nothing, but this is a belief on which sufficient evidence for a decision has not been gathered in the North. Deaths from rabbit-starvation, or from the eating of other skinny meat, are rare; for everyone understands the principle, and any possible preventive steps are naturally taken.'"
I lifted that from here : https://en.wikipedia.org/wiki/Protein_poisoning#Observations