I have Norcold so I may not be much help, but did you verify power tro the refrigerator and did you verify everything else electrical is working like normal.
I got confused when you say "when you came back after 5 hours you turn the Fridge back on"? Are you saying you have only on & off switch? When off nothing happens but when on the Auto Light comes on? Seems like it should have some way to let you know if Fridge is running off propane or electric?
Our unit allows Propane only, Electric only, Both (will use Propane only if no Electric) or Off.
Basically we never turn the Fridge off (unless at a gas station), it is otherwise always on Both. Had it been us, when you unplugged to leave, the propane indicator would have came on and ran for the 5 hours.
When we returned and plugged back to shore power the Electric indicator would have come indicated the propane was off.
Sometimes there are delays and we may see a red light but after few minutes it switches to the correct power source.
I am gonna assume you got all of this down and doing the right thing, if so a defective control boards is all it can be.. But I think it is odd you can't just turn for Electric only