My daughter's laptop had a similar problem. It was an over-heating issue.
Download a free CPU-thermometer tool (such as at
www.CPUThermometer.com) and have it running whilst using the laptop. If the temperature is getting really high each time it freezes or cuts out, that's your problem.
A short-term solution is to make sure that you use it on a hard, flat surface to allow ventilation.
My daughter's turned out to be that the CPU heat-sink wasn't attached properly and the jointing compound had dried out and was breaking away.
If that's your case, it can be as simple as carefully scraping the old compound off, replacing it and making sure that the heat-sink is attached properly. I'm sure you must know someone that could do that for you? I expect a repair shop would charge a fortune.
Hope that helps.
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