Sounds like you're getting air in the propane line to the fridge that the furnace purges when it's running, or the gas flow to the furnace lowers the pressure enough to let your burner operate correctly. Have you pulled the burner and inspected? If you look at the flame when it runs, is it blue or yellow? Blue when the furnace runs, yellow when it kicks off - replace the burner.
A word of caution - be prepared to also replace the tubing to the burner. Chances are you will kink or twist the existing aluminum tubing when you try to detach it from the burner. I replaced mine with copper and new fittings.
Jerry & Jeanne
1996 Safari Sahara 3530 - 'White Tiger'
CAT 3126/Allison 6 speed/Magnum Chassis
2014 Equinox AWD / Blue Ox