Stabiltrak codes can NOT be read by consumer OBDII scanners for the simple reason that they are not emissions-related.
They can be read by high-end scan tools of course, and here's an interesting tip: they can often be read by code scanners that can read ABS trouble codes. I have a dedicated Actron ABS scan tool that can read Stabiltrak codes and, with the firmware upgrade, can also reset them.
I also have an OTC scan tool that can read OBDII, ABS, SRS and Stabiltrak codes. Look for a code scanner than can read ABS codes and you can also probably read Stabiltrak codes.
By the way, the dealer who told you that the codes were erased and could not be read, was lying. ABS, SRS and Stabiltrak codes are stored in history until erased by a high end scan tool, no matter how brief or intermittent.
Or the other alternative is to assume that nearly every intermittent Stabiltrak code that goes off after a short drive and a reset is a steering wheel position sensor. It seems to be the nature of the sensor, in that most of our driving is straight ahead, and thus the outer edges of the sensor get used little. If the vehicle is parked for a day or two, especially with the steering wheel off center, the computer detects no contact, shuts down Stabiltrak and sets off the code. Once you drive for a bit, it makes good contact and a restart shuts the code off. It is the nature of the sensor itself, and this is why a new one will fix it - for a few years anyway, until it starts to get a bit corroded on the contacts outside the straight ahead position. It is much like the 4-wheel-drive switch that needs 'exercising' a few times a year to make good contact.