Stalling while idle.

Hello,
The car runs quiet well except when you're at a stop. Occasionally it will do a rough idle or it will go from a smooth idle to stalled. From keeping track it's mostly a smooth idle and then stalls out. I've noticed that sometimes the car tries to save itself and it will go from almost stalled to idling normal. Usually if I hit the gas (if it goes to a rough idle) all is well, and the car will be fine until another prolonged stop; around two minutes. The car will start right back up with NO hesitation. Once the car is above a few miles it's fine, even if it went from a rough idle to moving. Has no real problem accelerating whether it's on a flat street or going up a hill. I had them run a test at Auto Zone when my check engine light first came on and they said it was bad gas. I ran the car to almost empty and used fuel cleaner and have started using better quality gas. It improved a bit but the car still stalls.