My sister-in-laws fridge did the same thing. I can figure a lot of stuff out, I did everything I knew to try, finally called in a buddy who is a certified RV tech.
Sounds crazy but the final result was the cooling fan on her 120/12 volt converter had failed. The converter was over heating and dropping voltage. Without the full 12+ volts the propane solenoid wouldn't open.
I put a new cooling fan on it and it was fixed. That was 2 years ago and its still going strong today.
There are 24 hours in every day - it all depends on how you choose to use them.
Bruce & Jill Brown
2008 Kountry Star Pusher 3910