It happens to lots of people, and the solution is to determine what
software is the cause. Use Task Manager, leave it open and set to
Processes and Sort on CPU. The the one with the activity is the culprit.

It can be dependent on the monitor you have. My Viewsonic monitor does that
from time to time, I just turn it off with the soft-off when I'm not gonna
be back for a while, because according to MS there's nothing you can do
about it.

We just got new computers a couple months ago, and I figured a fresh
install would resolve it... but nope, even with absolutely nothing
installed but Windows, the power management still fails to turn off the
monitor. Only on my computer. My wife's Acer monitor turns off just fine.

Windows XP's power management is buggy on some systems (it's a known issue
according to MS, and it's not going to get fixed). Like my laptop, it likes
to put it into standby, even though standby is disabled, and occasionally
it fails to wake up the monitor when resuming from sleep state.

The problem is in its idle monitor. Occasionally it fails to detect the
system being idle, and won't turn on the screensaver, or turn off the
monitor. And with some monitors (especially CRTs), occasionally it will
randomly bring a monitor out of standby and show the screensaver. I've seen
it happen on flatscreens too, but it's a common problem on CRTs.