I have a cat who does that. He was almost bald in spots on his back. That distressed me. Took him to the vets. He's on kitty Prozac which has worked for him. It's about $50 for 2 month supply but he has fur and I'm less stressed about him. Vet said it was a cat form of OCD or like picking at your skin as some people who have OCD do. He was stressed out from "The Holy Terror" aka our new kitten, Lily. She loves/lives to torment him.