It really sounds like you face the same temps and arid climate that we face here. My peonies do increase slower than others here on the forum--I don't have nearly as many first year blooms as most, but they do increase and they do bloom. I have a feeling your issue is planting depth. Plants in pots aren't necessarily at the correct depth in the pots--I've replanted several tree peonies that had to go much deeper and herbaceous that were planted too deep in the pot--had to remove soil from the top when they were planted in my garden. I'd dig yours up in the next few weeks, if the leaves have started to turn brown it's the perfect time. Check to make sure the roots are healthy like Karen said, and replant so that the eyes on the tops of the roots are no deeper than 2" below the surface. If you mulch heavily (I do, too, in my climate) you'll want to make sure it's more shallow over your peonies. The fertilizer that Karen suggests, BulbTone, has made quite a difference in number of blooms for me and it's not very expensive and easily found both locally and online. Azomite helps quite a bit with stem strength as well.
