Circuit/System Testing
WARNING: This page is about a different car, the 2008 GMC Yukon XL, 2008 GMC Yukon, 2008 Chevrolet Tahoe, 2008 Chevrolet Suburban, and 2008 Chevrolet Avalanche. However, it is still accessible from the selected car via links, so may be relevant.
Check for EBCM DTCs as an incorrect speed sensor reading could cause this issue. If no other DTCs are found then refer to Transfer Case Disassemble to inspect for possible clutch damage.