The same problem happened to my 07 I5 and it was a bad encoder motor. The motor was seized up so the shift fork never moved.
The shift fork is said to be a weak point of the transfer case, but if it's just blinking and returning then I would not expect the shift fork to be the problem.
Easiest solution, you have a stuck selector button on the dash. First bump and jiggle each of the buttons and see if any are stuck down.
Next, you can check for other things.
The transfer case is a 'dumb' system in the way that it doesn't actually just what gear it is in, it only knows what position the motor says it's in. In my case, because the motor wasn't moving, the gear was never shifting.
If you had a case where your car is telling you that it's going in 4LO but it doesn't feel any different, then there is probably a problem with the shifting fork, or at least somewhere inside the transfer case.
Here's the post where I talk about it more.
http://www.hummer4x4offroad.com/for...nsfer-Case-Control-Module&p=204757#post204757
In summary, you can test the motor yourself if you have a 10mm socket and wrench, it's very easy to remove, inspect, and reinstall.
Just pull off the four bolts and see if it is rotating when you hit the dash button.
The replacement encoder part number
is GM 89059688, at least on my 07.
Let us know what you find!