Something similar to this happened to me a year or so ago. Fridge just wouldn't run on gas, but was fine on electricity. I had a company tech look at it while I was at the Good Sam Rally and after the second "repair" didn't correct the problem, the tech replaced the electrical board in the refrigerator. Problem solved! The best part of the whole situation was that I wasn't charged anything for the repair even though it was out of warranty.
This was my second experience with a refrigerator acting up and working some of the time and not others, and both times the problem was solved by replacing the electronic board. I have no idea what those boards cost, but the techs always tried some other "simple" repair without success and finally replaced the boards. Problems solved.
2016 Eagle 323 LKTS
2009 GMC 1-ton Dually Diesel