07 GMC Yukon liftgate will open, but not close automatically

Door ajar switch possibly . The lift gate not working is a different matter . Could be any number of thing's .
Power Liftgate System Components
• Liftgate motor assembly
• Liftgate latch
• Liftgate module (LGM)
• Liftgate side upper sensor - left
• Liftgate side upper sensor - right
• Liftgate handle switch
• Liftgate close switch
• GMLAN serial data link
• PWR LIFT GATE 30 amp fuse
• PLG 10 amp mini-fuse

Your best bet take it to a qualified repair shop that has the diagnostic tool that can communicate with the lift gate control module , too check for DTC'S - diagnostic trouble code's .
Liftgate Module
The liftgate module controls the liftgate motor, liftgate clutch, and liftgate latch based on various inputs. The liftgate module also performs diagnostics on these inputs and outputs and will disable liftgate functionality and set DTCs should a fault be detected. The liftgate module is secured to the motor assembly at the left rear of the vehicle. The module requires a liftgate position learn procedure be performed when replacing. This allows the module to learn the full open and full closed positions of the liftgate.

DTC B153A 00: Liftgate Latch Switch Signal Circuit
DTC B153A 08: Liftgate Latch Switch Signal Circuit Signal Invalid
DTC B153B 02: Liftgate Open Switch Signal Circuit Short to Ground
DTC B153B 05: Liftgate Open Switch Signal Circuit Open
DTC B153E 02: Liftgate Position Sensor Signal Circuit Short to Ground
DTC B153E 05: Liftgate Position Sensor Signal Circuit Short to Battery or Open
DTC B153E 08: Liftgate Position Sensor Signal Circuit Signal Invalid

This is not a job for a diy'er or vehicle owner .

Unless you have electrical diagnostic skills , I suggest you take this to the dealer ! The lift gate can be opened by operating the switch on the instrument panel. Battery voltage is supplied to the liftgate actuator through the body control module (BCM). The BCM will pulse the lift gate actuator when a release input is received through the key fob, or the instrument panel switch.
The body control module (BCM) receives an input from the liftgate ajar assembly. The ajar assembly is normally open when the liftgate is fully closed. When the liftgate is opened, the ajar assembly contacts close providing a path to ground. The driver information center (DIC) illuminates the rear access open message when the gate is open. The instrument panel cluster (IPC) receives a serial data message from the BCM indicating the liftgate ajar status. If this message is displayed and the vehicle speed is greater than 8 km/h (5 mph), a chime will sound.
It could be ajar switch is bad .

chevy tahoe lift gate not opening - YouTube

? 2:12
www.youtube.com/watch?v=xU6ybiY3F4I
Sep 1, 2010 - Uploaded by 76bluemoon Back lift gate/glass would not open or release. ... Wow, are you sure? .... known issue with tahoe, suburbans, hummers and othergmc vehicles. ... 2007-2012 Yukon Denali Rear Door Lock Actuator Replacement ... 2004 GMC Yukon XL rear liftgateremoval - Duration: 50:17. by Velvethamma 5,814 views.

You should still be able to open itmanually? Unless the lock is not functioning. There may be a plastic plug that pops off on the inside of the liftgate panel so that you can open it. You have to remove the plug and then move the lever with a screw driver. All that being said most likely have some broken wires in the boot at the top of the liftgate where it connects to the body. These wires tend to break from constant flexing when the liftgate is opened and closed. Either way you have to get the liftgate open to inspect them

It can be faulty switch or its issue with lift gate latch.Its got stuck up hard or cracked inside.It has to be inspected.-----------
There are few help links with proper solutions for these problem.I suggest you to refer the links.
Click the link below:----
2007 Mercury Mountaineer: Liftgate will not Unlock or Open? http://whoisbyme.blogspot.in/2012/06/2007-mercury-mountaineer-liftgate-will.html
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Adjust Hydraulic Lifters? http://schematicsdiagram.blogspot.in/2012/04/adjust-hydraulic-lifters.html
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How to open rear lift gate? http://repairhelpcenter.blogspot.com/2011/12/how-to-open-rear-lift-gate.html

--------- Power Liftgate Shuts Down http://whoisbyme.blogspot.in/2012/07/power-liftgate-shuts-down.html
------------ Power Lift Gate Will Not Remain Open http://whoisbyme.blogspot.in/2012/07/power-lift-gate-will-not-remain-open.html
----------- Power Lift-gate will not Operate http://whoisbyme.blogspot.in/2012/07/power-lift-gate-will-not-operate.html
------------- Liftgate will Not Stay Up Open? http://whoisbyme.blogspot.in/2012/07/liftgate-will-not-stay-up-open.html

---------------- Rear Door will not open http://whoisbyme.blogspot.in/2012/07/rear-door-will-not-open.html
------------ 2000 Toyota Corolla: Rear Door wont open from outside or inside? http://whatisbyme.blogspot.in/2012/05/2000-toyota-corolla-rear-door-wont-open.html

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These details will help.
Thanks.

check the shocks, they may be bad

Problem may be stripped gears i engine. I had to replace the entire mechanism several months ago. Gears are not metal.

try removing your shocks/struts for the lift gate. once removed, check to see if they fully extend in and out of the barrel. You may have bent shocks/struts. Also, check to see there is nothing preventing the lift-gate from opening such as a bolt or acorns between the spoiler and the roof...

Sounds like bad spot in gear,will require replacing mechanism.