OK I have pictures now.

They don't have some sort of borer? Have you looked closely for insect damage in the affected stems?

The soil looks like recently cultivated. The pictures in fact look like they've been recently planted in new bed. Did someone damage the roots? Extreme watering? Herbicides?

One of the stems on the second picture is some kind of gray. Fungus? Do you clean all foliage in the fall and how crowded they are? If it is botritus you have to get rid of plants and soil.

In reading about peony disease, I think it is the verticillium wilt! Where there is no cure. Isn't that great!!!! NOT!