I've had this problem on a 2000 Mountaineer (same as the '01 Explorer) I purchased. What usually happens is that with age and dirt the latches on either side of the lift-gate start taking more effort to unlatch. This puts additional strain on the yellow plastic clip that attaches the exterior handle to the linkage that opens the latches. This causes the yellow clip to break or pull out of the handle.
The way I got my lift-gate open so I could repair it was to open the rear window and stick a long screw driver down inside the lift-gate. You will need to distort the plastic interior trim in order to force it over the window latch in order to see what you're doing. Warning: This may cause the trim panel to crack at this point, especially if it's cold. I warmed mine with a hair drier and in my case it did not crack. This may be easier to do if you first remove the inside pull-down handle and a single screw which is sometimes found under the smaller plastic cover near the rear window latch.
Standing behind the truck, look down into the center of the lift-gate, you will see a pivot with 2 metal rods leading to the left and right latches. Take your screw driver and push down on the left side of the pivot point and the latches will open. Be ready to open the lift-gate while the pivot is still pushed down.
If you want to know how to fix the lift-gate so it will open normally again, just ask. You will need a new yellow clip and a can of spray lube.
