I'm in the process of fixing the same problem on a GSS22JEPDWW right now. There are several parts in the defrost circuit that I can tell:
1) Defrost Heater
3) Temp Sensor (Thermistor)
4) Main Control Board
I've replaced the Defrost Heater (remove back panel of freezer section - it's a stainless steel bracket that has a glass bulb in it) and it still doesn't work. The main control card provides power to the heater 4 times every 24 hrs for 25 minutes or so to defrost the evaporator coils. If all items are working, you'll see water in the drip catch at the bottom inside of the freezer compartment. Better yet, pull the refer away from the wall for 24 hrs and check if water is gathering below the plastic drain on the right rear of the refer in the pan. The water drips into a pan and the fan for the condensor coil evaporates it. Go to the www.ge.com
website and look in the service section to find the parts diagram for your refer. You can then get a part number to buy the parts you need from a local parts store or the Internet.
I just bought the thermostat a few minutes ago and will try that next. Heater was $37, thermostat was $15. Sensor is about $20 and the control card is $140 (you can find on line for $95). I'm going down that path. If none of this works, it'll be in the dump in a week.
I've learned on-line GE refers are bad news. The control cards can fail repeartedly, althoough mine has worked for over 4 years. But, I won't ever buy another one since refers should last at least 15 years in my book. After $200, it doesn't pay to throw more good money after bad. I'll keep you posted on my results.