According to the owner's manual, the recirculation should not be shutting itself off until de-selected manually or at the next key cycle (2012 GC Manual, page 404):
Pressing the Recirculation Control button will
put the system in recirculation mode. This can
be used when outside conditions such as
smoke, odors, dust, or high humidity are present.
Activating recirculation will cause the LED in the
control button to illuminate.
Continuous use of the Recirculation mode may make
the inside air stuffy and window fogging may occur.
Extended use of this mode is not recommended.
The use of the Recirculation mode in cold or damp
weather could cause windows to fog on the inside,
because of moisture buildup inside the vehicle. Select
the outside air position for maximum defogging.
The A/C will engage automatically to prevent fogging
when the recirculation button is pressed and the mode
control is set to panel or panel / floor.
The A/C can be deselected manually without disturbing
the mode control selection.
When the ignition switch is turned to the LOCK
position or the ignition switch START/STOP button iscancelled.
cycled to OFF, the recirculation feature will be
Mine never has and just for grins I tried it at lunch by putting it into recirculation (it also always turns on the AC, so I pushed the AC button off). Drove for over 15 minutes and it was still on when I reached my destination. Repeated on return trip.
I accidentally turned on the recirculation on a trip this past spring and forgot to shut it off, until almost an hour later.