It is possible that your system’s resources are being shared and used by another application. To check, open Task Manager and go to the Performance Tab to see how your resources are being utilized. If you are seeing high utilization, you may have to close other applications that are currently running in your system. Go to the process tab, select non-essential applications that are using high resources, and click End Task.
If resource utilization is still high with only Game Center running, then this may be an issue with your hardware.