Issue appears to be fixed. Based on everything I have read on the forums, there are a lot of things that can cause the Stabilitrak error with no apparent rhyme or reason. People have reported that their fix was a variety of things including spark plugs, spark plug wires, throttle body, MAF sensor, brake light switch, fuse #9, and PCV leaks. The horror stories are that many people spent upwards of $1000 or more at the dealership with no resolution. I was a mechanic for 21 years but changed careers in 1989, well before this system was put into place. However, I decided to tackle this problem anyway. I have an OBD2 scanner but there are no codes set and nothing beyond normal on the reading. I checked for vacuum leaks and found two cracked PCV hoses but that did not fix the error. After consulting with someone else and the lack of troubleshooting guidance and the fact that the truck has 190,000 mile on it, I thought the next logical step was to replace the wheel speed sensors. Almost $300 later the issue still exists.
I posted my dilemma on the Avalanche Fan Club forum and someone responded that I needed a scanner that will read the ABS system. I had no idea that there was a different scanner to read more information. Instead of buying a scanner, I went to my local Auto Zone and they scanned my system and found there was an ABS code #C0267 - “Low Brake Fluid”. Really? The brake reservoir was a little over half full. On a normal system that is perfectly OK. You only need the fluid in the reservoir to fill the space in the calipers as the pads wear. Anyway, I topped off the master cylinder and the error is resolved.
Bottom line: Take your truck to Auto Zone and get the ABS system scanned for codes before you start throwing parts at it.