Apple - Constant kernel GPU panics (GPUPanic.cpp:127) on mid-2010 MacBook Pro (6,2)

Repeated kernel panics occurring without third party drivers can only be caused by a few things:

1) A peripheral device

2) A bad OSX image or bug in OSX itself

3) A hardware problem

In your case, it is unfortunately (3):

System model name: MacBookPro6,2

The kernel panic indicates that your GPU is failing. This is a known issue for your machine. Your model is subject to a replacement program for the logicboard due to a defective GPU. It lasts 3 years from the date of purchase. If this is already expired, Apple may or may not still replace your logicboard. It is ultimately at the discretion of the store manager. If you don't qualify, your other option would be a flat rate repair, for ~$300, which Apple will repair anything wrong with the machine for this fee. Best of luck.

Yes the GPU panics are almost certainly due to a defective discrete GPU card. I have the same 2010 MBP and have noticed 10.9.3 has increased the frequency of these fatal crashes significantly.

I'm using the gfxCardStatus utility to turn off this discrete card whenever possible but many apps force it on.