In my original Dometic fridge, the pilot light
was also going out. Also, the electronics just puts up the "Check" light but does not retry igniting it, until it is turned off and on again.
In my case, I replaced the electronic board with a 2nd source Dinosaur board.
However, the real basic problem in the original Domectic fridges is that, while one terminal of the thermocouple is connected directly to the board with a push-on terminal, the other terminal is connected to the ground block, separate from the board, also with a push-on terminal. These connections are EXTREMELY sensitive to ANY resistance in the connections, as the voltages generated by the thermocouple is in the 25 mV range, that's 25/1000 of 1 Volt! I would suggest removing and cleaning these thermocouple connections and crimp them a bit after reconnecting. Even in the non-electronic controlled fridges, the thermocouple connections are very critical.
My bet is, dimes to donuts, that is where your problem is.