Do you feel any sort of misfire coming from your car? (Mine has had a misfire issue for a year, and I can tell you exactly when it does it because I feel it when I'm sitting there in the drivers seat.)
A year ago, I was exactly where you are now. A stalling issue that gave no codes whatsoever (although it ALWAYS started right back up). We changed the fuel filter (hubby guessed on that one), and for about 2 days there was no stalling. She FINALLY threw a code (I can't remember when, but I know it was at least a month later) for random misfire (or multiple, or whatever it is....I have it all written down somewhere but don't feel like digging for it lol). My hubby works at a body shop that has all kinds of scanners and stuff, and we were able to determine that the misfires were only on 2 of the 4 cylinders (again, not sure which 2), so we changed all 4 plugs with autolites. I would have preferred AC Delco's, but the local dealership was already closed for the day at this point, and if the issue could be fixed relatively quickly, I was all for it.
Not fixed. A few weeks later, the CEL came back on. The hubby was tired of messing with it, so we took it into a mechanic (local, not GM). Mechanic diagnosed it with alldata and determined it needed a new coil pack. A few weeks later it was STILL doing it, and alldata pointed to new injectors. Still nothing. Mechanic and I started wondering if the autolite plugs we'd put in were just junk from the factory, so he put in AC Delcos. Still nothing, although she finally did stop stalling and acting like stalling (BUT the weather got warmer).
All summer, I have had zero stalling issues, but my CEL will come on for a while and then go off. My hubby has a cheaper scanner that I've confiscated to just keep in my car. The code has always been the misfire code. There are a few times that the misfire has been so bad that the whole car kinda shakes from front to back, but it's only when I'm at a stop, and throwing it in neutral corrects it. A few weeks ago, around the time that it was only 40-50 degrees out at night in my area, she started acting like she wanted to stall, but hasn't gone that far. I have a feeling that here in about a week when the avg. high in Ohio is about 30, she'll be stalling out constantly, and with the nice bonus/overtime check I'll be getting from work, I'm going to cave and take her into GM service. :-(
Sorry this is so long, and hopefully your stalling issue won't cause you the headaches that mine's caused me, but if you get any codes, look out, and in all honesty, just take it to Chevy. I've probably spent as much already as I would have had I just taken her to the dealership in the first place.