The vet ruled out leukemia or immunodeficiency virus. Her calcium is high, so the probable diagnosis is some kind of cancer. The vet gave her a shot to boost her immune system. She gets one of those a week for about a month. He also gave us a series of three pills to give her over the next three days. I gave her one at home; she promptly threw it up.
Her prognosis is a much-shortened life. The vet says cats usually only live 3-4 years after diagnosis. So, who knows. I'm pretty depressed about it, but we'll take care of her for as long as we have her, and more than that one cannot do. Other than her vomiting, she doesn't seem to feel bad. Poor kitty.