Even with an alternator if your voltage regulator fails it can cook the battery. Overcharging as suggested in the post by Dale Leonard can kill a battery. Have you ever smelled a sour smell after a long drive? Is there an indication on the underside of your hood of bubbled paint; it could be an indicator of boiling battery acid fumes from overcharging. I would suggest checking the voltage and/or amperage from the output side of the regulator at a running r.p.m. say 2000-2500 r.p.m. You would normally find about 14 to 14.5 volts running at that speed. Much more that 14-14.5 volts would be excessive.
good luck, I hope you are able to solve the problem soon. john