OP:

Is this issue happening with a clean install of windows 7?

Does it do it from the start of your gaming session, or does it do it when you've been playing for a few minutes or longer?

By your PC specs, using an older cpu with a new graphics card, I'm assuming you built the machine yourself? What you're describing strongly sounds like either a CPU throttling issue (where it gets too hot and clocks itself down).

Also, is the 960 GPU the 2gb or 4gb model? Curious because the 4gb models probably suffer the same fate the 970 does when it accesses the last .5 GB of memory because that last .5 runs much much slower and will cause what you described, but you'd be needing to be running higher than 1080p resolution, and I'm not sure what you're running at.

Answering these, even if silly, will help me try to answer and diagnose your problem.