I'm having exactly the same problem so I went to the GE website and read the manual for the TFX20SA side-by-side refrigerator and found nothing that describes this problem.  There is heading under the Customer Service section called "GE and You, A Service Partnership" with a paragraph that states, "you can always call the GE Answer Center at 800-626-2000, 24 hours per day, 7 days per week".  I called the number and was told they don't answer questions, but rather simply call someone to come out to your house to fix your unit!  What lies they publish!
I did find a website describes how the defrosting system in a generic refrigerator works and how to troubleshoot the components that might be failing.  The webaddress is:
www.appliance411.com/faq/howdefrostworks.shtml
I intent to try to fix my frig using their advice since GE certainly won't give me any!
                
 John Peck
                
 November 2007