When you turn the fridge off and turn it back on can you hear the igniter trying to start the flame? Can you see a flame from outside with the cover off? You should be able to see and hear the flame. Do other propane appliances such as the stove work? Is your battery in good shape? The fridge cools with propane but the mother board in it needs a good battery state of charge. A dead battery would kill the fridge. If the battery is strong check your blade fuses to make sure it isn't something simple.

Somewhat common with RV fridges is the circuit board failing. If that's what it turns out to be and you are outside warranty install a dinosaur board. These are aftermarket replacement boards that are built better than factory. We have a dometic fridge and I am going to order one to keep with us when we travel as a replacement I can install on the road.
https://www.dinosaurelectronics.com

I had the same thing with my water heater. I good hear it clicking but only for 3 seconds. Was able to light it with a lighter but flame would go out after a few seconds. It was the circuit board failing. After replacement it was fine again.

Hey thanks. It's an old fridge (2006 Weekend Warrior toyhauler) so this is to be expected. I'll pursue the circuit board route. My batteries are fine so sounds like the board.

Appreciate your input.

As a follow-up. Turned out to be corrosion on the burner element and a regulator not working (was only registering an 8 instead of 11 on the manometer. A cleaning and a new regulator solved it.

Good deal! Glad you got it fixed up.
Happy Trails!!!

Cleaning and inspecting the burner element is now a part of my annual trailer maintenance. The Norcold unit in my trailer is 19 years old and still going fine on both electric and propane. We use the trailer about 5 months a year total, with a mix of boondocking, RV parks with utility hookups, and state and federal campgrounds with and without utilities.