Battery Draining...

Trying to figure out if my 1 year old camper just came with a **** battery or if something else is going on. We purchased our new trailer (Outback 325BH) last July. I noticed that if it sits for more than a week or so the battery is dead forcing me to connect to the truck before I can get the power jack to work. At first I noticed that I was leaving the TV amplifier on so I blamed that but it still happens when I shut it off. This camper has the in command system for lights, tanks, slides with a screen on the wall, so my next suspicion is when you hit power off it's only the screen that goes off (Similar to an iPad) so I now hold off and actually power down the system but it still seems to drain. Turned on the fridge the night before our last trip just to find it warm in the morning because the voltage dropped too low for the ignition over night.

Any thoughts on how I can tell if something is draining the battery vs just having a crappy battery? I would think it was new with the camper but who knows.

Thanks!