I have an 08 Tahoe and am experiencing this same issue.
It started a couple weeks ago when the battery wouldn't start. I was able to jump it, and it drove fine for a couple days, then while I was driving one day, all the electrical displays in the dash and stereo began to flicker and when I turned off the car, it wouldn't start again.
So I had it towed to the dealer, they said it was a bad battery. A week later, the same thing happened. I had it towed back to the dealer, they charged the battery and said everything looked fine. I drove it back home, turned off the car, tried to restart it and it wouldn't start again.
Same thing, I had it towed back to the dealership, and now they're saying it's starting fine for them and they can't find anything wrong with it. It really sounds like something's draining the battery when the car is off.
Have you guys got your issues resolved, and if so, what did the dealer do to correct it? I have to drive from Maryland to New Hampshire next week, and I need this car fixed asap.