I also had this problem. I have a P4 1.3 from Gateway. Their technical support was unable to help and even though I have long since abandoned ME, I am curious as to why it was happening.
I had every power management tool disabled (including those in BIOS)! More often than not, the system would go into stanby while I was surfing the web.
Not sure if this is the same as Kurt's prob - my system was unable to wake up! Ctrl-Alt-Del didn't even do it. Had to power off and restart...