It shouldn't go dead that quickly. I had issues when I first bought my car (was a 1 year old CPO) and they first changed the cable that goes from the front of the car (battery) all the way back to the engine. However, 6 months later, I had to change the battery. I don't drive mine now for a couple of weeks and it's fine. The only thing I notice is I have to use the key to unlock it (remote key thingy doesn't work).

 

No problems.

I just went out of country and my 2009 was parked in my garage for 4 weeks (29 days to be exact) without being fired up or driven. I got back, unlocked it manually with the key, used the remote to disable the alarm, got in, and it fired up just as it always does. I did then take it for a proper 30+ minute drive.

So if your battery drains in under a month I'd bet there are things pulling power that should not be, or your not letting the battery charge by driving (eg you have lots of short trips), or the battery is just too old (but mine is 4 years old and just fine)

 

Other than what's already been mentioned, you may have just gotten a defective new battery when it was replaced and one or more of the cells are dead. Any decent auto parts store or Firestone dealer can hook it up and let you know if the battery will hold a charge or not.

Hopefully, it's just something really simple.