Update: I gave the peony a little shade with some cardboard, but more importantly, I gave it a slow deep soaking so that deep layers of soil were well moistened. The plant perked up. I suspect that before, I was watering superficially, and it was probably dry at deeper levels where the roots were. I'm not sure why the other peonies were doing ok--I thought I was watering them all the same.
I guess when there is a stress placed on plants, often 1 plant shows the stress first.
