I found a solution (at least, it works for me).
Go to Settings -> Battery Manager -> Battery Mode, and change the mode to anything but "Maximum Battery Saver". That stopped the problem for me.
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Ironically, the problem only seems to happen with the Maximum Battery Saver profile. The problem doesn't
appear to happen during off peak times in a custom profile, but I only did a quick test.
Originally, when I switched from a Droid to a Droid 2, I used MyBackup to backup all my phone settings. I then restored them on the Droid 2. I thought that perhaps using settings restored from older hardware was causing the problem. So, I then backed up everything on my phone except the settings, did a factory reset, and restored the phone. The problem no longer happened.
But, then I went through all the phone settings to manually set them to how I wanted them to be. After doing this I noticed the problem came back.
Eventually I narrowed it down to the battery saver setting. I can very consistently make this problem happen with Maximum Battery Saver, and make it stop happening by selecting another profile.
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Do An Experiment:
Maybe other people could test. Try the following experiment:
1. Settings -> Battery Manager -> Battery Mode -> Maximum Battery Saver
2. Plug the phone charger in.
3. Turn off display with power button or just let it turn off on its own.
4. Unplug the phone charger.
5. Does the backlight come on and stay on (the screen stays blank, but the backlight turns on; sometimes you have to look closely or be in a dark room)?
Then:
1. Settings -> Battery Manager -> Battery Mode -> any other profile
2. Plug the phone charger in.
3. Turn off display with power button or just let it turn off on its own.
4. Unplug the phone charger.
5. The display should not turn on.
Post your results here.
I have started the same discussion on droidxforums.com
here.
J