I had a very simlar problem with the misses car doing the same thing. After 2 new batterys and 4 weeks of diagnosing the problem, it ended up being the stezza causing the battery to drain flat. The Stezza worked all good with no problems but when you put a volt meter on it to see how much current it was pulling with it just being on standby with no ignition key on, it was pulling stupid amps from the battery killing it.
Im not sure if this is any help but do a test by disconnecting the + battery lead and by putting a multi meter between the + battery terminal and the battery lead with the ignition turned off and all doors closed because your interior light will draw power dont forget. You should be able to set your multimeter to show amps and then know what its drawing. I belive that it should be no more than 0.08 or 0.1 of a amp. If it is more than this, you have a problem or short somewere which is killing the battery.
Alternator is the only other thing you may wana check. It also may have a problem not charging or it has a short too. You just dont know till ya check it out.
If you havent got a multimeter, get one mate coz they are a very handy tool to have. If im not even close to what your asking, just say