There are parasitic draws on the battery bank even though you have turned the battery bank off via a switch. Over one or two nights these parasitic draws, such as the CO monitor, draw very little however over a week the draw adds up.
Was the inverter left in 'automatic' mode, meaning that it comes on when there is no other AC power source? An inverter draws power simply being in 'idle' state.
When all else fails, follow the wires.
US RV base, MD
2007 Alpenlite 34RLR