Sounds like you have a draw on the battery that it running it down, and, possibly damaging it. Batteries do appreciate being run right down. If you can test the cells individually, that will give you a good idea as to its health.
Do you have an ammeter?. With everything off and doors closed, disconnect one battery post and put the ammeter in series between the cable and the battery. Anything over 40 milliamps is not good.
What's the voltage across the battery at idle? At 2000 rpm?