Yes. Mine will usually open after working the up/down switch a few times though. There is actually a TSB for this.
TSB 07-20-5
10/15/07
REAR POWER WINDOW MOTOR
INOPERATIVE/STUCK IN THE UP POSITION
FORD:
2002-2005 Explorer Sport Trac
2002-2006 Explorer
LINCOLN:
2003-2005 Aviator
MERCURY:
2002-2006 Mountaineer
This article supersedes TSB 07-16-14 to update the Part List.
ISSUE
Some 2002-2006 Explorer, Mountaineer and 2002-2005 Explorer Sport Trac, and 2003-2005 Aviator vehicles built before 1/23/2006 may experience a rear power window that sticks in the up position. This condition can be intermittent and may be due to the power motor which temporarily locks up.
ACTION
Follow the Service Procedure steps to correct the condition.
SERVICE PROCEDURE
1. Use the current Workshop Manual (WSM), Section 501-11 procedure to remove the door panel and inspect the window regulator for damaged parts.
2. If any damage part or parts are found replace the regulator assembly.
3. If no damaged parts are found on the regulator assembly, replace the window regulator motor using WSM, Section 501-11.