Does it work OK on electricity and not shut off? If it does, you could be right about air in the line. Does the stove work OK on propane. Also, I know it seems obvious, check that you have propane (don't ask why I suggest this
)
If all the other propane items work OK and the frig has the same problem on electricity that is has on propane, I would suspect a control board issue or a problem with your 12vdc going to the frig.
Dave
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Dave, Barb, and Paisley the Wonder Wiemeraner
Was - 2015 3160RL Legacy Edition & 2014 F350 6.7l PSD SRW Platinum
Now - SOB