I have an 8560 with the same or a similar problem. I've noticed that it's related to the CPU &/or MB chipset cooling fans coming on.
What happens for me is the laptop just shuts off. The strange thing is, XP Pro doesn't think the system ahs shut down erratically - normally what should happen is when the OS is booted back up, it should want to run a chkdsk on the hard drive after an erratic/unexpected shutdown. After the shutoffs that I have, the OS boots normally, as if the system was shut down normally.
Another system I have discovered is that when I have a movie DVD in the drive, the laptop doesn't seem to die. Go figure? The only thing I can surmise is that the extra heat produced by the DVD drive keeps the fans on. If the fans stay on, maybe a power surge or whatever is happening when the fan(s) come on is not happening.
If anybody has any suggestions, please post them here.