Control Panel, Device Manager, Monitors, right click on your monitor then click Properties. Under the General tab Windows may tell you that your monitor isn't working properly. If this is the case, try

Check your monitor settings (my Viewsonic monitor has an auto off option that will turn it off regardless of whether it is in use or not)

Update the monitor's drivers (if it came with a disk from the manufacturer use those drivers instead of the generic Windows Drivers.)

Check your Power Plan:
For Windows 7
Go to Control Panel, System and Security, Power Options. under Preferred Plans, pick whichever plan and click Change plan settings. Choose how long before your monitor turns off.
If you want a screen saver to run instead of just going dark, right click on your desktop choose personalize and note or change your screen saver (it is in the bottom right corner).

Check your motherboard settings.

Check your graphics card's settings (though I've never heard of a graphics card that did what you've described).

Hope any of these help.