could be issue in the propane line. could be regulator. I assume the stove will blow full power on all 3 burners???
Possible the pipe to the fridge is blocked mostly, will build up decent pressure when fridge is off, will burn good on that pressure for a while then flames out. I have heard of pipes being blocked like this and even the oil filling the low places doing this. There is an oil in the propane tanks that can get into the lines...
More likely there is issue on the fridge itself. The thermocouple could have issues, and for a handy guy can be a cheap fix. Burning a flame is not rocket science so whatever the issue it can be fixed. As long as the fridge does work on electric then the fridge is good.
