My mini fridge has full power, but I come home after a couple of days to find that the compressor has shut off and everything has defrosted and the fridge isn't cold anymore. I can turn the knob and in about 15 minutes it's back to ice cold. Does anyone know whey this keeps happening? I don't want to just toss it if it's something I can easily correct.
Check that the cooling coils are clean and dust free. vacuum if needed. If the coils are dirty and unable to release heat it may make the compressor over heat. Or if it has a reset switch the power will be cut out before it reaches critical temperature.
It is probably a bad thermostat.
A thermostat can be tested by shunting it. Wait until the problem occurs, then connect the two wires that go into the thermostat. If the compressor goes on, it means the thermostat is bad and should be replaced. The thermostat is inside a box attached to the back. It looks like this:
Alternatively, it may be inside the fridge itself if the fridge is larger.