Here is a TSB that might apply:
Bulletin No.: 02-01-39-007B
Date: November 05, 2007
INFORMATION
Subject:
Automatic Dual Zone HVAC Battery Draw
Models:
2004-2007 Buick Rainier
2003-2008 Cadillac Escalade Models
2002-2008 Chevrolet TrailBlazer
2003-2008 Chevrolet Avalanche, Silverado, Suburban, Tahoe
2002-2008 GMC Envoy Models
2003-2008 GMC Sierra, Yukon Models
2002-2004 Oldsmobile Bravada
2003-2008 HUMMER H2, H3
2005-2008 Saab 9-7X
Supercede:
This bulletin is being revised to add models and model years. Please discard Corporate Bulletin Number 02-01-39-007A (Section 01 - HVAC).
When diagnosing battery draws on trucks equipped with the automatic dual zone HVAC controls (RPO CJ2), technicians should keep in mind that the control head does not completely “go to sleep” until after 150-250 minutes, or up to 4-1/4 hours, from when the ignition key is turned OFF. This is a normal condition. In these cases, DO NOT replace the control head.