Engine

When was the last tune-up? Any applicable trouble codes? To check codes yourself, at the least, you need an obd2 code reader. Some of the national brand autostores used to check codes for free.

Does it stall at idle or runing down the highway-- hot or cold? When it stalls, does it restart quickly?

Autozone usually will check codes for you. Did they give a reason why they couldn't check codes?

When you try to restart, is the security lite on or flashing? When the problem occurs, have helper crank it, while you check for spark at the plugs. If you have spark everywhere, use a gage and check fuel pressure. Check for fuel injector pulse, also, engine cranking.