My mirrors lately have been somewhat intermittent, so I sometimes wonder if the switch itself may be out to lunch.
Here is a way to test the voltage to see if it is working through the body harness to switch.
See 06 factory Service manual.
http://www.colorado4wheel.com/manuals/Jeep/KJ/2006-KJ-SM.pdf
You have to remove the power mirror switch I believe section 8 describes removal etc.
Then Disconnect the wires/connector from back of power mirror switch.
Next then switch ignition to the run position...
Connect a 12 volt test light, to Pin # 5 in the harness connector at mirror switch.
Touch the test light probe to pin #3.
Hopefully then the test light illuminates, proving that the wiring circuit between the battery and switch are fine.
By chance if the lamp doesn't light up, then check the fuse 25 which is located in the junction block.
If the junction block fuse is good, then it is time to start looking for potentially a wire with poor continuity/broken.