Try to disconnect the thermister. It's the white wire that runs into your fridge and is usually connected to the fin inside the fridge. On the back of the fridge it should have a two wire plug. I had this problem and was ready to buy a new fridge. Found out the thermister was bad. When it's disconnected the fridge should run constant.
If it starts working.. then you need a new thermister. Or.. you can just run it that way. It could start freezing everything but I have found that usually with normal use the thing can run constant and not freeze up.
Good luck.
Another thing to check.. On the back of the fridge. You will have to open the outside compartment. See if the heating element is working. If it is you probably have a bad cooling element and then might as well replace fridge altogether. If it's not then could be the elec heating element or the thermistor. Or even control board. But first step is to see if it's heating.