Monitor enters power save mode while playing games (and sometimes other times too)

I have a Dell Alienware x51 r2 which has had ongoing display issues, which have mostly been resolved. But the continuing one is sometimes the screen will go dark and enter power save mode. Audio continues to play, but I don't seem to be able to alt-f4 out of whatever I was doing.

I run cpuid monitor periodically; it is not connected to any overheating. I have my power management set to never put the computer to sleep or turn off the display. I have tried opening the case and blowing everything out with canned air. It does not happen with just one game, and has sometimes happened when I'm doing nothing more system-taxing than reading stuff on the internet.

If I try to adjust monitor settings, it tells me my computer isn't sending a signal. Unplugging the monitor from the computer and plugging it back on does not resolve this.

What further troubleshooting steps should I be trying?