Did you run other games and/or 3D Benchmarks successfully for more than 45min? Usually this kind of problem is due to faulty hardware (possibly combined with driver issues). You can also use a temperature monitor for your graphics card to monitor GPU core temperature. You are describing a very likely symptom of excess heat. A quick google also shows some issues with badly seated heatsinks on 7770s.
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Casy * Foreign Secretary * Alliance of HonorIntensive Care Bear