My 15 year old Kenmore appears to be on its last legs. Plug it in and it gets cold, down to -10 in the freezer. It works for about 12 hours and then warms up. I believe the compressor is not coming on at that point. Turn it off and let it sit a day and it will work again for 12 -24 hours.
The compressor is thermally protected. My guess is it's getting too hot and cutting off. After running for 24 hours, the compressor is very warm to the touch, and I can hear a switch or solenoid on the side of the compressor clicking every several seconds. I doubt it's worth fixing, but thought I'd throw the question out.