If your have the coach plugged in then Yes you may leave the inverter/charger turned on. A lot depends on where you live. If you live in a very cold climate and totally winterize it then I would be sure the batteries are full of water and fully charged and then disconnect the ground cable then let it sleep for the winter.
I keep our plugged because I keep items in the refrigerator. Our coach is stored in my insulated garage/barn only 50 feet from our back door.
It is helpful if you lets us know what kind of RV you have then we will have a better idea of what we are dealing with and someone with the same RV may have had your same issue.
Charging house batteries
in Electrical
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We have a 2007 United Specialties