1. Go to www.cpuid.com
2. Download HWMonitor from there.
3. Install it.
4. Run it.
5. Play the game until it starts lagging.
6. Minimize it and look at temperatures. For best results, take a screenshot.
7. Tell the temps to us.
I suspect it might be an overheating problem. Follow the steps above to find out whether it's what I suspect.