Adding to my earlier comment, I suspect as other people have commented that a baking stone can yield inconsistent results. I started preheating my oven to 520 a good 30 minutes before I was ready to bake. (My oven thermometers-- yes, I have two of them --indicate that my oven temperature is about 20 degrees cooler than the oven's temperature setting.) I preshaped the pitas and gave them a 15-minute rest before rolling them out and letting them rest for another 15 minutes. I know some bread recipes call for preheating a stone or Dutch oven an hour before baking. The pitas might be less likely to puff up if the stone hasn't gotten hot enough. It's getting hot enough here in NC to the point where I might try grilling pitas indirectly in a very hot grill.

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