What type of peonies did you plant? Fernleaf and fernleaf hybrids go dormant pretty early when newly planted. Another thing that can be a problem is water--too much is bad. If the roots get waterlogged they will rot. If planted in a boggy area you should move them. If they were underwatered they can go dormant early, too. As long as the underwatering wasn't severe they'll come back fine next spring, though (I've done that one myself!).

If none of the above ideas seem to fit you might want to post some pictures so we can get a better idea of the situation.