I'll assume you don't have it set to turn off after X minutes of inactivity and your battery shows it is charged. Try turning it upside down and check to make sure the cooling fans are turning. If not you may be able to get them running again by blowing out the dust with canned air. If that's not it we will try something else.
Two things come to mind in this situation as previously suggested. Heat and battery. Try plugging your laptop in to an ac adapter. Then run the pc on AC power. If it is still going out, it may be overheat. Dont stick the pc on things that block the vents in that case, if the pc stays on in ac but goes out unplugged then the battery is probably bad and it sounds like a few years have been put on the battery if it was never changed so it may just be a bad battery that can be replaced by ordering a new one from toshiba. I dont know abut your satalite model but in the manual, mine says the battery charge lamp will blink green and amber when plugged in to indicate bad battery. Do not think this is software related unless it was always the same time or after a certain period of time every time. Then i would check software. Try sitting the pc on a table or somthing (even a cooling dock would do) run it on there and if you dont shut down then somthing is blocking the cooler, if the pc is shutting down on bat but runs fine plugged in then its a battery issue.
Unless the laptop is configured by your settings to shut off, randomly shutting off is usually caused by a hardware problem; rarely a virus. There are several freeware utilities you can use to test if it is a hardware problem. You can download Speedfan http://www.almico.com/speedfan.php to monitor temperatures and voltages. Speedfan is notoriously inaccurate on some systems, but you can report back here what you find with it. Memtest86 http://www.memtest.org is a useful tool for testing memory. And Prime95 http://www.mersenne.org/freesoft.htm is a CPU and system stress tester.
Is it plugged in when this happens, also i am thinking of another avenue, do you have a toshiba power utility on your machine (the icon is a hand holding a battery in the system tray or the area next to the clock)? If so check the settings as it could be an enabled setting in there.
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