It sounds like you are running out of power, in other words voltage is dropping low enough to shut down the furnace.
The voltage in the battery will creep up enough to start again, then when you restart, it drops again.
I am guessing you are not hooked to shore power, or your batteries are not getting a charge.
Have you tried to run the heater with the engine running?
Happy Glamping.Norman, 2008 Winnebago Adventurer 38J, W24, dozens of small thirsty ponies. Retired after 40 years wrenching on trucks! 2010 Ford Ranger toad with bicycles or KLR 650 in the back. Easy to spot an RVer, they always walk around with a screwdriver or wrench in one hand!