Car Stall problems of the 2007 Saturn Aura

The vehicle's engine shut's off while in the "on" position and moving. The electrical stays on, just no engine power and no warning lights. Worst of all, can not recreate the problem. It can happen a couple of times in a week or it can go months before it happens again. Went to two different mechanics & neither one can re-create the problem. You lose the engine, power brakes, & power steering and the car is still coasting along. Like trying to a fly a plane with no propeller. Since the car is coming into or going out of a "stop" position, you can be travelling through an intersection after coming from a "stop" lose the engine, & now you are stuck in the intersection. Action is to roll to a stop without getting hit. Put the car in "park". Turn the switch to the "off" position even though the engine is already off & restart. Approximately 10 times (+) this has happened since oct. '13. The car isn't on the gm recall so they won't look at it. They want a mechanic to find the problem, but a mechanic can't recreate the problem. The dealership doesn't want anything to do with it. I believe this is the 2nd time I have filed this complaint, it has happened more since the 1st time. This is a gm Saturn Aura. The ignition recall is only for Saturn ion. I have no idea what to do. All I want is a safe vehicle. Until today's event, is the car wants to stall/shut off before it does. So you get a warning that the car will shut off. Helps prepare for the inevitable stall + gives me a chance to record the stall. I have at least two videos of it occurring. The norm has been, coming into or out of a "stop" position: 1) wants to shut off but doesn't, 2) very shortly thereafter at a "stop" position - the engine will shut off, and 3) restart the car, 4) (not always) shuts off again at another "stop" very shortly thereafter, and 5) not happen again for some random period of time.