Dig a root and see what it looks like then report back. There is a disease that causes collapse in several plants but I think you will find that the roots have been either eaten away below the ground or have been undermined by the voles so that they have not been in contact with the soil except at the edges of the plant. You may need to replant

Thanks for your response. After I posted this, I watered for a long time and the peony recovered, but I suspect that deep down there is some vole/mole activity which added to the problem because, as I posted, none of the nearby plants are suffering.

Even though the roots are not being eaten they may be suffering from the tunneling causing much of the roots to be in air. Pick a safe distance away from the peony and probe to see if there is a lot of open space in the soil. Al

I think that the roots probably are being exposed deep down, but there's very little I can do. The bed is heavily planted, and my gardens have HUGE rocks in them that the moles/voles like. I know that area has been a mole haven for years before voles moved in as well.

Do what you can to collapse the tunnels. I would shove a hose down a hole made with the probe into a tunnel area and turn on lots of water while continuing to probe in the area and collapsing the tunnels. Al