With the car in Park & idling - Check the voltage across the battery terminals. IF the voltage is like 14.7, then the alternator is fine. Then you start checking the wiring around the battery for a loose connection. IF the voltage is like 12.0, then the alternator is your problem.
Sounds more as though your alternator is being to fail.
bad alternator
That battery light came on the other day so obviously it has something to do with that battery (duh) but do you think there are any other underlying causes? The car continues to run once the electric goes out so we're able to park it. But it won't start up again. Dunno much about cars, be nice!