Thank you for your detailed replies.
From your initial question I had about 7 different things that came to mind, yes a crank sensor came to mind but I eliminate that based on your replies.
Everything on this car is controlled electronically, ............it either uses battery voltage, sends a signal based on voltage ot resistance or completes a path to ground to operate.
Your traction control/ABS system is a system that is VERY sensitive to voltage. If the voltage is not perfect it shuts down and causes a indicator light as you describe.
You stated you alredy had a mechanic check the car, I will assume at this point that he connected a scan tool and checked for codes related to inputs sensors/etc...that would have caused this. So let's eliminate sensors/etc.....
Fuel pressure is not likely, if the car suddenly shuts off and will restart with no issues at speed then pressure is not dropping.
I'm thinking voltage at this point. Either you have a loose connection, corrosion or an voltage issue from the battery or alternator.
If the battery terminals are both clean and tight, the alternator connecions are good and no issues found with corrosion then lets move on. The battery needs to be connected to a battery analyzer, not just volt and load testing, a full dynamic scan. Same for the alternator, they commonly fail on these cars and have a regulator built in. You are most likely going to find that the alternator is intermittently acting up here baed on your inputs and comment of battery light coming on. Personally I recommend a genuine ac delco alternator, aviod remanufactured aftermarket units on this sensitive car.