I have a Kenmore model 25358689890 refrigerator that has stopped cooling the fridge side. I then need to turn it off and defrost it and restart it to ge the fridge to work properly. How do I figure out what needs to be fixed in the self defrost cycle?

Sounds like a faulty defrost timer motor. See if you you can find the defrost timer. It will probably be a small black box about 2 inches square, have 2 to 4 wires to it and will have a hole in the center with a shaft that you can turn with a screwdriver. The slot in the shaft for the screwdriver will only let you turn it one way. It will probably be in the compressor compartment. Sorry, but finding parts break downs for Sears appliances seem to be impossible now that they are owned by K-Mart. They want to be paid for them. Replacing is quite simple if you can find it, two screws and reconnect wires. Not very expensive and can be purchased at most appliance parts dealers.

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" I have found that the fridge is gibson fridgidare.. If the defrost timer is bad will the fridge run for about a month b-4 it needs unthawing? Or do I have other issues"

The amount of time for ice to build up depends on humidity and number of times door is opened. Sounds exactly like defrost timer or defrost heater to me. Timer is cheaper, go for it first.