...or an alternator "overcharging" problem has occurred, which could cause the same symptoms (as it had on mine).
Get an OVM and check the voltage across the battery terminals with the engine on (accessories off) and engine off.
Should read 12V when engine is off and ~ 14.4V when engine is running. Anything much lower than this indicates a charging problem. Mine was an overcharging problem, and my voltmeter read 17.5V!!!
If your belt tension is okay, you may just need a new regulator. Your car is an early enough model year that you can replace just that portion of the alternator (mine is internal, so I had to swap the alternator
).
Typically, it may be that the brushes are worn...