The next time the monitor goes black, shine a strong light on the screen. If you can still faintly see what was showing before going black, you are have a problem with the backlight in the LCD panel or in the power supply for the backlight. Unless the monitor is still under warranty or you are familiar with troubleshooting and repairing electronic devices down to the component level, it will probably be cheaper to replace the monitor.
Otherwise, can you test the monitor and its video cable on a another computer?
Otherwise, can you test the monitor and its video cable on a another computer?