Maybe the frost free part of the fridge has had it ?
From howstuffworks.com:
A frost-free freezer has three basic parts:
A timer
A heating coil
A temperature sensor
Every six hours or so, the timer turns on the heating coil. The heating coil is wrapped among the freezer coils. The heater melts the ice off the coils. When all of the ice is gone, the temperature sensor senses the temperature rising above 32 degrees F (0 degrees C) and turns off the heater.
Sounds like yours doesn’t know when to turn on. Time to get out that purchase slip and warranty and see if you can sort something out if it’s not too old