Just prior to shut down can you hear the hard drive doing a hard stop? (click).. This is important as some of these models have an issue of the 3.3V dropping out and causing shutdowns. Also download Mobmeter utility and watch the CPU temp prior to shutdown..
Has anyone had experience with this Sony notebook that sometimes shuts down after a length of time. All settings are set to desktop, so there should be no shut down. Sony had a bulliten to address this issue to other models, but not to this particular one.