Could be several reasons. Start with having the codes read. The codes will guide you towards the cause.
relay switch on dash is not ingaging tran case
The 2010 Chevrolet Suburban has rear wheel drive.
The 2004 Chevrolet Suburban has rear wheel drive.
The 2005 Chevrolet Suburban has rear wheel drive.
The 2002 Chevrolet Suburban has rear wheel drive.
The 2014 Chevrolet Suburban has rear wheel drive.
The 2009 Chevrolet Suburban has rear wheel drive.
The 2001 Chevrolet Suburban has rear wheel drive.
The 2008 Chevrolet Suburban has rear wheel drive.
The 2012 Chevrolet Suburban has rear wheel drive.
The 2011 Chevrolet Suburban has rear wheel drive.
The 2006 Chevrolet Suburban has rear wheel drive.