When propane is low or almost out, my heater will act funny, similar to what you are describing. It will attempt to fire, the burner will kick off, but stop very quick then. After the third attempt and it's not getting the gas, it will stop trying and kick off completely. At that point I have to turn the thermostat into the "off" poisition and then back to the "on" position. It will attempt 3 more fires or kick-off's and then stop completely again. My camper is very consistent, and fortunately, I run only one propane tank at a time, keeping the second one turned off all the time, so I know when one is empty and they both are not empty at the same time.
When the battery is low, mine will fire, but the fan will run real slow, until it just putters out. Eventually, it just makes a little click and doesn't do anything. If I am plugged into shore power, even with a week battery, the furnace will still run OK. I got a new battery last Fall. With power plugged into shore power, the furnace ran fine. As soon as I unplugged form shore power, the battery had no juice, and everything in the camper (lights and all) just went extremely dim. The furnace literally shut down.
My suggestion? Check your propane before doing anything else.
