After screen turns off, monitor stops responding

After screen turns off, monitor stops responding

I have 2 monitors connected to my computer running Windows 7 SP 1. If I
leave my computer for a while, Windows starts the screen saver (which for
me is just a black screen). It is not in sleep mode; I have that disabled.
However, sometimes when I wake my computer back up, one of the monitors
stops responding. I cannot turn it off with the button on the front, nor
do any of the other buttons work; it just completely stops responding. The
power light is still on on the monitor though. The only way to get it to
work again is if I unplug it for a couple of seconds, and plug it back in.
It doesn't always happen to the same monitor, I have had it happen both
monitors. (Not at the same time, though) It only happens rarely though,
maybe once every 2 weeks or so. This is very inconvenient, and I was
wondering if anybody knew why this was happening and/or if there is a way
to fix it.