Why wount 05 4 runner rear hatch not shut - 2001 Mazda Tribute

hatch jammed.
or weak motor.

Sounds like the sensor inside the rear latch. Most vehicles don't use an actual door switch these days.

Yes, had the same problem on my 05, The mechanism that operates the latch can fail, this part costs about $300 dollars and is only available at the dealer but you can save the labor and do it yourself.

push rear hatch to closed position to release locking mechanism

This is extremely common!
The micro-switch inside the glass hatch release is faulty, telling the door that it is partially depressed, thus shutting down opening for safety reasons.
You can verify this by opening the glass hatch (there is a access panel at the bottom of the door on the inside), removing the trim cover from behind the glass handle (two philips screws and one plastic push in fastener), then unplugging the glass handle.
Your door will now function normally, but without glass opening ability until you replace the handle.
The handle only takes a few 10mm nuts to remove and can be changed in a few minutes. It retails for around $35 from your dealer.

A VW dealership can change the programming for you with a VAG-COM device.

Turn on the rear window wiper . Try to get the wiper arm off the glass. There is a switch that will not let the window operate if the wiper is on the glass.

http://www.ncttora.com/fsm/2000/index.html has lots of great info...hope it can help... i have a 4runner my self but have not come across that prob...will the key fob unlock all other doors? do you live where its freezes...ive had doors freeze shut for weeks....

the bumpers could be worn from a lot of use but on a 05 i doubt it. there should be adjustment on the reciever 'post, joe