Hi,
What condition are your batteries in? Are they topped off with water every month or so? What kind of charger do you have? What year and length is the RV?
Yes all of that matters in figuring out the problem.
My suggestion for now might be a Olympic 6000 Btu Catalytic heater. It will warm my 30' Bounder with dual pane windows without any 12 volt power used. I only need to run the furnace a little bit - like 10 minutes per hour, when it is below 25F outside.
So the answer is not run your furnace at all!
Also consider installing some solar panels. If you add a pair of 120 - 150 watt panels to the roof, then the battery will stay charged the whole time you keep it in storage, and you should start the evening with a full battery.
My suggestion if the battery is not holding a charge is to replace it with a pair of golf cart batteries. They are slightly heavier, have more lead and water in them, and hold about 220 amp hours per pair. This should be plenty to run the furnace all night long, unless you have a large load such as a CPAP machine.
SunElec.com is a great place to find $1 per watt solar panels.
CampingWorld.com is a great place to look for the Olympic Catalytic heater. Mine has the optional leg kit, quick disconnect, and dust cover. Dust that settles into the pad can shorten the catalyst life, so best to cover it and store in the closet when not in use.
Good luck,
Fred.