Ok, you should have a Charge Indicator lamp on your instrument cluster. Does this light come on?
Either way, it sounds like your altenator is not producing enough power to run the systems on your car. If no major current draw items have been added to the car, like subwoofers and amp, or special lighting, then I would say it is time for another altenator. With the engine running, the altenator should put between 13 and 14 volts on the battery. If it is only putting 12.6 like you said, then it may be charging enough to turn off the charge light, but not enough to runs the car systems and keep the battery charged.
Also check the ground cables and engine grounds for corrosion and loosness.
Saturday, July 15th, 2006 AT 2:17 PM