I just recently had the same exact problem you're having: "Service Stabilitrak" message on startup, and only on startup. I did research and found this thread to be the most helpful:
http://www.camaro5.com/forums/showthread.php?t=136845
A couple people mentioned leaving the key in 'On' position and letting the system go through its paces and waiting for all the lights to turn off before starting, so I tried that first (Prior to this I always jumped in and started the car right away). To my surprise, it worked... but not for very long.
After that solution stopped working, I was confused but decided to try the solution of holding the key in start position until the car starts completely rather than just flicking the key into start. So far this is working and I have not gotten the "Service Stabilitrak" message since *knock on wood*.