This was my issue and my fix. But I do agree with the PSU issue too. First give a simple clean up a try and try some of the free suggestions before going out or a new PSU.
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He has another thread in tech support section and we came into conclusion that it's a CPU overheating issue.
http://forum.square-enix.com/ffxiv/t...11#post1373211
I was having troubles when I started and first thing you should do is run memtest. It checks to see if your ram is faulty. Turns out I had bad ram. That caused my comp to shut down. Otherwise make sure you installed the correct drivers for your graphics card.