I had this shutdown problem with my last laptop, I spent a vast amount of time trying to solve it and I never did. In the end I sold the laptop (to a windows user who wouldn't notice it because it worked in windows). My new laptop is fine. During the process of troubleshooting, the concensus appeared to be that I had a buggy DSDT (differentiated system description table) although I never managed to fix it and trying to gets you into some pretty deep water.
Sorry this is not more positive.
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).