Dometic Penguin II - cools, but compressor cuts on and off

There could be a freezestat stuck between the coils of the evaporator causing this issue. And the capacitors are another possibility.

The freezestat prevents the indoor coil from frosting over and completely stopping the flow of air through the coil. When the compressor stops with the fan running, the ice melts and compressor restarts only to have the coil freeze up again.

If it's a capacitor, the internal overload on the compressor could be overheating and breaking the power for the motor until it cools.