One problem related to transfer case has been reported for the 2006 Chevrolet Silverado. The most recently reported issues are listed below.
My truck at speeds around 35mph while letting off the accelerator it would jump out of gear. So then, in 2012, I had the transfer case actuator motor replaced and it fixed the problem. Then just yesterday (oct. 31, 2014) I had cruise control set at 70mph and when it would coast or try to slow itslef down to maintain its speed, I would here a clunking noise and it would jerk. When I let off the cruise control and would let it roll to a stop it would pop out of gear! I made it back to town and even at slower speeds it would jump out of gear to the point where I had to put it in 4wd high to be able to move. I spoke with a mechanic at the local dealership and he said they have a lot of problems with them like mine which is why I think there needs to be some attention brought to them.