Might the battery is not being charged, the alternator is not putting out full currant/voltage. This could be the reason the battery want dead. Use a voltmeter to see if the battery is receiving 13-14V during charging. A charged battery should have a voltage of 12.6-.8 volts. If below 12V it is dead. If you have a battery charger, charge the battery fully and see if this makes a differance.