Welcome!
Nearly every "LPG" Appliance in your RV needs 12-volts-DC to operate it. Fridge does, furnace does, most water heaters do, and if you have a wall thermostat, so does your rooftop A/C.
It'd be helpful to know if your coach is plugged into a shore tie pedestal or home outlet while this problem is happening.
Make/Model of Furnace would be good to. No biggie, but when you said "Heater" I was thinking of the one in the dashboard that you use driving the coach.
I hate to tell anybody to run out and spend the $100 or so that even a basic single RV (or "trolling motor") battery is gonna cost. That said, a lot of trouble gremlins hide in a "House" or "Coach" (as opposed to Chassis) battery.