What would cause multiple fridges motors to stop running, but leave the lights on?
One possible explanation for this would be if you run the fridge from batteries or solar power with too small inverter. Even a small fridge requires an inverter capable of giving at least something like 1 kilowatt when the motor starts. If the voltage drops when the motor starts, it won't be able to start spinning after the initial pressure pulse of the first rotation: the motor will get stuck and the overheat protection will cut the power from the motor. After a few minutes the motor will again try to start, and possibly fail again.

This answer does not apply if the fridge is connected to proper AC mains power.