There is an idle sensor within the Throttle Body which becomes dirty from carbon. Two things: Add a can of that Carb cleaner to a tank of gas, I know it's not supposed to have a carb but it works and second, try spraying a cleaner, they have a spray cleaner in auto store for this purpose, directly down the throttle body, under the bonnet and wipe as well as you can with a rag, working it in as far as you can. Once the sensor is clean, the stalling will stop.
The 2014 Jeep Grand-Cherokee has rear wheel drive.
The 2004 Jeep Grand-Cherokee has rear wheel drive.
The 2009 Jeep Grand-Cherokee has rear wheel drive.
The 2013 Jeep Grand-Cherokee has rear wheel drive.
The 2008 Jeep Grand-Cherokee has rear wheel drive.
The 2006 Jeep Grand-Cherokee has rear wheel drive.
The 2003 Jeep Grand-Cherokee has rear wheel drive.
The 2011 Jeep Grand-Cherokee has rear wheel drive.
The 2005 Jeep Grand-Cherokee has rear wheel drive.
The 2007 Jeep Grand-Cherokee has rear wheel drive.
The 2010 Jeep Grand-Cherokee has rear wheel drive.
The 2001 Jeep Grand-Cherokee has rear wheel drive.