Thanks, y'all. She's indoor only, and she's only had this issue since we moved down to NC from VA. It started after we'd been here a few months. So it seems like it could be some kind of local allergy.
StarryEyed, I like the idea of a medicated bath--but I doubt she would cooperate with that at all. I've only given her one bath several years ago and it became very clear that she had not been bathed as a kitten, as she objected mightily. I may try again, though--do you mean the regular Aveeno packets for humans?
Hell603, The vet did suggest that perhaps it might be a behavioral/stress-related thing, and that Feliway might be worth a shot, but nothing has changed in her little world for a very long time, so we can't fathom what could be bothering her. And she is otherwise behaving normally--she doesn't seem anxious or upset. If I tried the Feliway, do I have to get enough to cover the whole house, or is one room enough? (She wanders at will.)
Cearbhaill, what do you mean by "good oils" and how do you get them in the cat?