Any clues? I got my galaxy on Monday and it works well until the next day. I installed Big Planet, barcode scanner, rmaps, and offline google map files (~430MB), and updated to II4, but it shuts off while i was working. The battery should be reinstalled to make reboot possible. I tried rrautane's solution (killing every app before locking the screen) and it seemed to be effective. Now I think the phone may not wake up (and no response) under certain condition so I let my phone never lock the screen, it's battery consuming but gets no random shuts.
And I found something else about the battery. With 3G/GPRS/Wifi all turned off, no background data/synchronizing and screen auto-locking turned on, my galaxy will only eats about 1% battery in one hour; but if it idles for a long time (i.e, while i was sleeping at nights and no other one will use my phone), the battery will be consuming in an incredible speed, about 60% in 6 hours. I think maybe some programs are using CPU, but I cannot catch them.
Sorry for my poor English. I really love this phone but something still needs to be solved....