Over Charge problem?

Run a voltage test on the battery while the vehicle is running and find out the voltage that it is kicking into the battery. Could be a new alternator to you but it could be rebuilt and done poorly. Consider the voltage that you get but the issue is also whether they alternator is continously charging and thus overcharging meaning that the voltage regulator is not working properly. I really suspect the alt because the wiring is hard to mess up.