I have this problem with my 2012 mini. I think the blackout happens when the mac is unsure about what resolution should be used for the monitor and tries to renegotiate with the monitor.
I don't have a workaround for newer OS than 10.9.5. but this may give you an idea.
My workaround is to go to Displays Preferences and set the resolution to Scaled with the same resolution as native, i.e., my monitor is 1920x1080 native, so I choose Scaled 1920x1080 to get optimal viewing quality.
But normally the mac won't easily stick to that setting and will revert to "Best for display" when I quit the Displays Preferences. Probably it thinks why not use Best For Display when that Scaled resolution is the same as native.
The trick is to choose a lower resolution such as 1600x900 then change to Scaled 1920x1080 back and forth for a few times. I will know it has stuck when the screen goes black for a longer period (a few seconds) than usual during switching back to Scaled 1920x1080. After that the screen won't go dark by itself anymore until I boot from other macOS (or reset PRAM, perhaps).
IME, this trick doesn't work with newer macOS because the setting just won't stick.