a game that starts running choppy after 30-45 minutes could be a couple things, most likely in this scenario being heat. Check your computer area, make sure the vents of the laptop aren't being blocked at all, check the laptop itself and make sure that its fan is still running. If you have recently started playing in a different location, possibly setting the laptop on something like a blanket that might be blocking the vents, that could be your culprit right there.
Other potential issues include hard drive wear and tear. Download a free program called speedfan (http://www.almico.com/speedfan.php) and install it to check your computer temperatures and your hard drive SMART error status. check the temperatures when the computer starts running choppy and when its just first started up, and post both sets of temperature numbers here.
on the SMART error tab of speedfan, select your had drive from the drop down and look at the status bars at the bottom. IF either of them are lower than 90 oercent, you may have an issue.
Other things to check, bios updates for the laptop for better temperature regulation, blow the dust out of the laptop fan with a can of computer spray air, update the drivers, etc.