Usually because they are planted too deep. I plant mine so that the eye is not much more than two inches below the surface.

There are three common reasons.

The first, as Jen says, is that they are planted too deeply, but planting in too low light levels (i.e. in shade) will also prevent flowering for many species and varieties. The third reason is over-feeding - plants react by producing copious foliage but no flowers.

to add to Ilex's reply, Some species of peony are not very happy if they get sun first thing in the morning.