The Dometic cycling on and off quickly could be entirely weak undercharged sulfated batteries triggering the low voltage disconnect of the Danfoss compressor controller.
Combine that with too long and too thin wiring and the fridge might be perfectly operational, it is just the battery and the wiring from it to fridge which is severely lacking.
Most people have no idea it is bad to leave a Lead Acid battery sit in a discharged state. Many think all they have to do is drive for 15 minutes and the battery is magically restored to full charge and 100% health, when nothing can be further from the truth