Monitor goes into powersave mode randomly

My desktop monitor will randomly power itself down into power save mode while I'm working on the computer. The screen will suddenly develop a greenish tint before it says that no input is detected and immediately afterwards it'll go black. I've tried turning the monitor off and back on without success.

Connections have been checked and cords have been checked and all appear in working condition. I even checked the male and female connections to see if there was an issue there. I can shut down the monitor, unplug everything to the monitor, plug everything back, turn it back on, and it'll still say no input detected.

The only thing that seems to work is if I turn off or reset the tower itself. Then the monitor will work just fine until it randomly does it again. The time periods before this happens again have ranged anywhere from 5 minutes to several hours.