I know she is a different species, but Disney (my dog) does the same thing and it is due to allergies. The vet gave me a shampoo to wash her in and then prescribed 1/2 a Tavist (over the counter). Now that it is under control and she isn't licking her fur completely off I give her the Tavist every 2-3 days. She would lick her fur right off her legs and a couple of spots on her side and make her skin very raw. She still licks a lot and her white fur at those places stays a constant shade of orange/brown from her saliva.