How old are the plants? Young plants will sometimes make buds that do not develope into flowers. They simple stop growing and fall off. Al

That is exactly what happened with some of my newly planted peonies. For example, one new plant sent up 5 buds but 4 of them turn red, brown and die. Only one was able to bloom and even the bloom was somewhat deformed.

Peonies do fine in light shade but seem to grow a bit slower; I have 2 Singing in the Rain plants planted the same year, one under part shade (pine trees) and one in full sun. The one in full sun is finally going to bloom this year, shady one not so much. They also seem to be more leggy and less squat and bushy in shade.
I bet the buds drying up was just because the plants weren't quite mature enough to fully form blooms--you'll probably have a big show from them next spring.
If they're in heavy shade I'd think about moving them this fall, heavy shade will eventually kill them off.

Thanks, the plants are several years old. I think I'll move them this fall.