i have the same problem as you and i believe its a heat issue where when the laptop cpu gets too hot it shuts itself off so that it doesnt fry itself. i dont know what causes it but i pretty sure thats what it is. im hoping to put mobo monitor 5 on it to see what the tempes are when it shuts down to see if im right but i have to find out what motherboard is in my laptop first. you should give this a try maybe itll help you find out whats wrong.
2.8 p4 @ 3.15 900fsb, 4 sticks corsair xms cas latency 2-3-3-6 256mb each, leadtek 6800 gt 256mb @ultra speeds, gigabyte ga8ik1100 mobo, nec 3500a 16x dual layer dvd burner, tdk 48x cd burner, wd 74gb raptor hd, windows xp pro sp2, dell 2005fpw 20 inch widescreen lcd monitor