I'd bet the inverter is not on, either the switch on the inverter itself or the push button switch on the display on the wall.
Like others have said, unplug the trailer from shore power and open the fridge and see if the light comes on.
Also, like posted, I too have travelled 4-6 hours and my fridge is just fine. My fridge/inverter is connected to a seperate set of batteries that are NOT connected to the truck wiring, so they dont charge when travelling down the road and still lasts for a long time.
2017 North Point 375BHFS
2015 Silverado 3500HD Crew Dually Dmax 4x4