Likely a bad alternator or connections. Sounds like the alternator is undercharging the battery and you will have problems as the battery runs-down. Check the battery cables and make sure the connectors are clean and tight. There have been problems with the connector to the alternator, e.g., cracked wires near the connector.
Get the electrical check done, or as a start measure the voltage at he battery while the vehicle is running, and also when it is shut-off.
Light came on while driving home then I checked the battery (no more green eye) so assumed it was the battery(original...pretty good). Now I had stalling issues before all this(solved ) and I guess all the cranking I did killed it plus the colder weather. To clarify ...battery light came on .... replaced battery and light is still on after about 30 seconds to a minute after startup and stays on.
if it goes on and stays on for a short while after its started then randomly shuts off the voltage reg is starting to go and will trip only when theres enough voltage the alternator supplies... have the alternator checked...
if you have a multimeter attach it to the battery before a cold start and look at the voltage then have someone start it then look at the voltage again if it stays around 10-12 volts then shoots up when the battery light turns off the alternators your culprit
Happend to me early this year... The shop I use said the batt seemed ok but the alt was bad.. (along with other stuff)
I had him replace the alt, but found myself dead on the side of the road the next day... he towed me back and tried again with another alt.. he did this (free of charge) three more times... FINALLY he opted for an OEM alt and threw in a free Interstate bat at his cost... been working great ever since.