I originally thought of the itch thing, but since she's been doing it every time she goes to the food bowl--for about 5 hours now--I've ruled that out. When she's at the food bowl, she seems to do it when she wants to crouch her hind legs. That to me suggests it must be a problem in her knee. I hope she doesn't have luxating patellas, though I have no idea what the symptoms of that are.
I felt her leg all around, and she doesn't yelp when I move it in any position. I'll try massaging it and see what happens.