Your problem is the old NVIDA issue.
While its too late now to get it fixed from Apple as they have now EOF the system (May '13) so they don't repair or stock parts for this model any more. But, you will likely find a few Apple authorized repair centers still working on them and still replacing and/or re-balling the GPU.
You see, the solder its self is breaking down from the extreme heat and age. NVIDA also had a problem with the chip as it was overheating (not meeting spec) which Apple got them to cover their repair costs.
Getting back here to the repair: You need to get the rev2 Apple spec'ed part and replace your current GPU if you have the older out of spec unit. In any case you do want to take the GPU off and clean all of the solder and re-ball with the correct high temp solder.
Be careful with the fly-by-night outfits out there! Some just reheat the chip which will appear to work but will soon fail again as the solder has broken down which is why you need to clean it off and re-ball to do the job correctly. Besides, heating the logic board incorrectly can cause other problems. There is a method that needs to be followed so you don't damage other parts.