I have made pita twice recently, both times it stayed puffed after baking. I know when I have bought it from the store it was flat.
It tastes great, it is just difficult to store.
The last time I made them I put them in a bowl lined with a towel, and then covered the bowl with another towel. That seemed to help some. I cut the cooking time down from 6-8 minutes to 5. Going to drop the heat some tomorrow. I still have half the batch to bake for my pathfinder game.