How old is the dog? When Danes are still growing (until at least 18 months), they often look starved, despite the enormous quanitites of food they consume. Thankfully, once they hit full size, the food quantity levels out, and they fill out.

If the dog is not still a pup, she should see the vet, in case it's something more serious, and the vet can check out the falling-out patches of fur while she's there.