When you get it running again, I would put a volt meter across the battery terminals and check the voltage with the engine idling. I would then turn on the A/C (set blower max) and the head lights and see if the charge voltage drops below the standing battery voltage (battery voltage without the engine running and everything turned off). If the alternator cannot at least maintain battery voltage with this load on it, you probably have a problem with the alternator.

If you're having intermittent charge light, this could point to the voltage regulator on the back of the alternator. The voltage regulator supplies the ground reference to the charge light, and breaks this reference when the alternator begins charging. When the light is on, the battery is supplying 12V + to the alternator field windings. When the light goes out, this is because the alternator has started charging, the regulator breaks the ground reference, and the alternator from that point supplies it'own excitation voltage. It will continue to charge as long as the engine is running.