Sounds like it may be overheating. The laptop may be automatically shutting down to keep it from frying any components.
Try installing temperature monitoring software (Speedfan, Hmonitor, etc.) and have it log the temps. Then you can see if it is high just before it turns off.
If it is, and the laptop is under warranty, contact the manufacturer. If it isn't under warranty any longer, then carefully open it up and clean out the dust and debris from inside. This should help the temp. If that doesn't do it, the thermal paste may need replacing.
Also, if you don't feel comfortable doing all that yourself, I would then suggest taking it to a local tech.