The problem is most likely either the defrost timer, and/or the defrost heater element(s) are faulty. The problem is that the defrost heater elements are not functioning properly and the evaporator core is actually freezing up and blocking the air flow through the evaporator core and also freezing up the thermal sensor, and when that happens there is no longer enough cold air being circulated through the refrigerator (that is actually how the unit operates and air must be able to flow through the evaporator core and then be circulated throughout the refrigerator to properly function
) and as a result the refrigerator stops functioning and food can even thaw out in the freezer although the freezer seems to be iced up. (Usually at the rear wall where the evaporator core is located)
(Air flow through the evaporator core and cold air circulation and re-circulation through the refrigerator is performed by the air circulation fan and it also must be functioning
Be sure to only use a blow dryer (with a towel on the bottom of the freezer) to thaw out the evaporator core and do not use any hard or sharp objects or the evaporator core can be damaged. The defrost timer can be located inside of the refrigerator itself, (see lower image) or it can be mounted outside usually either behind the air intake cowl or kick panel at the front base of the refrigerator, or most likely located behind the service panel on the rear of the refrigerator, and usually if the defrost timer is turning then it is most likely working, however the defrost timer can move very slowly and you can place a mark on the timer and the housing to check after about fifteen minutes to see if the position on the defrost timer has changed. The deforst timer on newer digital models can be built into the circuit board and is not a seperate timer mechanism.
Here are some images that should be similar to your situation to help assist you, and let me know if you require any further assistance.