I am not sure if this will fix your problem but I ran into this same problem recently with my 07 LTZ.
Here is what happened to me.
1) The buttons were worn on my original unit, so I went out and looked for a new unit ( I found a brand new unit for $100 )
2) The New unit has a different part number than the original unit, I was told that the new part number replaced the old part number. the most obvious difference between the two (other than part number) was the top right button reads aux on the original and back on the new one, and I had the outside temp on the unit, as well as the outside temp on my mirror (they never read exactly the same, go fig)
3) I installed the new unit without any issue, plugged right in, I drove around for a few days. Then my wife and myself went for a date and she started messing with the AC blower, and all of a sudden it sounded like the fan was blowing hard, but I had no air, it had that sound of a blower in a box with no where for the air to go. We ate dinner and the problem was gone until we got to the theater. When we came back out it was fine until we got home and it started all over again...
4) I removed the new unit, took the buttons off and installed them on the old unit, and put the old unit back in with the new buttons and it has not happened yet to me.
Conclusion (up to this point): it may be the controller unit in the dash that is calling for air but not a door to open.
John