Have you had his teeth checked? I had a cat with bad teeth and some had to be removed. They can't clean their own teeth and they can't tell you when they've gone bad.
We had the vet look at him. I assume he thought of that. He gave us some allergy pills, which seem to help a little, so I'm thinking he was on the right track, but we can't figure out what he's allergic to. Probably us. Maybe our dog.