Hard to say. You need 3 things for the engine ot run, air, fuel and a spark. I wonder if something related to the automatic choke/idle system is malfunctioning. Althouhg if that was the case, you should still be able to start the car by manually opening the throttle with the pedal while you try to start it.

The other thought is that the alternator is bad and not recharging the battery. Are the gauges dead after the car stalls.

Look for more symptoms that relate to when it's running bad versus when it's running good.