My refrigerator would not work on propane when I switched from electricity to 12 volt. The stove would work but refrigerator gas light wouldn't stay on.
I had the same problem this weekend. Have never used fridge on propane, but plan to during upcoming long trips. I wrote down all of your ideas and will let you know if they worked.
I run my range burner on high for about a minute to purge all the air from the propane line, not had a problem with the fridge lighting if I do it that way.
2019 Dutchman Kodiak 293RLSL 2015 GMC 1500 Sierra 4x4 5.3 3.42 full bed Equalizer 10k WDH
As stated above if, not used for a while may take a couple of minutes holding the button in until the gas gets to the burner. If you have a pizzo-electric ignitor I have had sometimes difficulty igniting the burner with it and wound up using a standard grill lighter. In one case a spider had a small web insider the burner tube which prevented ignition - Cleaned out the spider web and it worked like a charm. Some of the fancier units have electronic spark ignitors and in that case it could be no power or a bad electronic module. Depending what system is on your unit it may be a relatively easy fix or perhaps off to the RV shop.
Is the battery charged? The fridge will shut off with low battery voltage.
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Ford Explorer or Chrysler 300C to tow with. Tracer Air 238 to be towed. Triumph Thunderbird Sport - with the toy-hauler gone it's at home. Retired very early and loving it.