Re: Problems with the battery draining in fifthwheel:
If you really want to know what is going on, put an amp meter in the positive line going from the battery. This will tell you how much the 'drain' current is. Probably the LP detector and if so equipped, the CO detector will take a bit. Any entertainment electronics may take a bit to keep the clock and memory going. And anything you left on (bay or closet light, thermostat, etc). As mentioned, even if you are not using any 120v, the inverter itself sucks up a bit.
The ultimate solution, of course, is to put an inline battery cut off switch in the line out from the batteries. May have to reprogram stuff when next you go to use it though. Don't forget that rechargable batteries 'self discharge' over time, so even with the cutoff, you will want to 'top them off' every few months or so.