I doubt your LP level and fridge malfunction are related.
First thing you want to do is make sure the burner is clean and the flue unobstructed. I had a piece of scale drop from the flue down onto my burner and cause all kinds of grief. If the gas jet can be checked, check it and behind it in case there's an obstruction there. If you are still having issues check the gas pressure.
In general the blinking light is a malfunction indicator.
I'm betting you hace a dirty burner like others have said.
2011 Itasca Navion 24J
2000 Chev Tracker Toad