It sounds to me that you are having a standard laptop problem, overheating. Gaming on laptops is the worst case situation, gaming puts a strain on the graphics system and add to that the poor cooling ability of all laptops, and the result is problems like you are having. You play games for a while, the PC get hotter and hotter, and the problem happens.
First, have you ever cleaned the dust from your laptops vents and fan? You should get a can of the dust cleaner and spray it into all the vents on the bottom and sides of your laptop. You must do a good job, the fan, heatsink, and vents are all small and dust build up happens very quickly on all PCs.
When using your laptop, do you have it sitting on a flat, solid surface? If it is sitting on your lap, couch, bed, or any soft surface, the cooling vents are blocked. Many laptop users do this and don't realize they are causing their PC to overheat.
If you check PC stores, you will find that Laptop Coolers are available now. You may need one of these to allow you to play games for long periods of time. All the things I mentioned are just the nature of laptops, and heat problems can be avoided if you treat them correctly.