I had a vexing issue the last few days with 1 of 3 external monitors on Mac OS X 10.11.6, where this one display would not wake up after the computer or display went to sleep. I switched around the monitors, unplugged and replugged them, and nothing seemed to help. I went to the point of disconnecting the monitor and replacing it with another extra display. This worked–to a point. Then, it happened all over again. I thought it was the port on the video card, since this is a Mac Pro with 2 cards. Eventually, any monitor plugged into this port would not wake back up after sleep.
Low and behold, I found a fast and easy solution–since it’s only been one time since the monitor has done this since I found the new trick, I can’t say for sure if it’s still a software issue, or a hardware issue, however, this trick worked to get the monitor lit up without unplugging or restarting:
1.) Go to System Preferences –> Displays
2.) Hold down the Option key and click on the “Gather Windows” button
3.) Click on “Detect Displays”
At this point, the sleeping monitor should wake right up!