In my rig, my inverter runs one circuit (a few specific outlets and the TV/blue ray.) One thing I learned the hard way (similar to how you learned it) is that also on that circuit is the fridge 120v outlet outside in the refer compartment. So if I run the inverter while the fridge is in auto, it will silently switch to AC mode which sucks my pair of batteries low enough to sound the inverter alarm before the movie your watching is over.
Might be your issue, worth checking. I now force the fridge to stay in gas anytime we are without hookups so I don't make this mistake again. Would be worth checking the water heater too. Things that take a lot of power but you may not notice are running.
