I don’t know why this would be happening, but to me, it sounds like you may have a voltage drop when the compressor kicks in. Can you hear the compressor start up when you first connect the fridge? Do you know if the fridges holds the temperature and runs fine for a while, and fails later?
Ideally, connect a volt meter as close as you can to the fridge and see if you see a voltage drop when the compressor kicks in. Even if you have a 10 ga wire, you can have a poor connection somewhere on the way to the fridge.
Alternatively, and this will be a bit destructive and maybe not something you feel comfortable doing, remove the cigarette connector from the fridge cable, optionally (but highly recommended) connect it to a 12v inline wire fuse, and then DIRECTLY hardware it to the battery, and see if that works. That’ll bypass any poor connections in your trailer wiring system. If it works now, you know it’s a wiring issue inside the trailer.
Ideally, connect a volt meter as close as you can to the fridge and see if you see a voltage drop when the compressor kicks in. Even if you have a 10 ga wire, you can have a poor connection somewhere on the way to the fridge.
Alternatively, and this will be a bit destructive and maybe not something you feel comfortable doing, remove the cigarette connector from the fridge cable, optionally (but highly recommended) connect it to a 12v inline wire fuse, and then DIRECTLY hardware it to the battery, and see if that works. That’ll bypass any poor connections in your trailer wiring system. If it works now, you know it’s a wiring issue inside the trailer.