Unfortunately this does affect Mac Minis. I have a Late 2012 2.6ghz Mini with 16gb ram attached to 2 Dell 24" displays - U2410 & U2413. I've literally done a bare bones reinstall of Sierra this morning and still get the black screen of death. This first started for me on 10.12.3 and still persists in 10.12.5
Things I've personally observed:
1. Mini boots to the U2410 (HDMI) but switches to U2413 (Thunderbolt to DisplayPort) in OS start up - this has always been the case regardless of version of Mac OS, but worth mentioning
2. Regardless of whatever else is plugged in to the other ports (USB, FW) after sleep for a prolonged period of time the U2413 display won't wake.
3. It seems to be a combination (in my case of which is the HDMI display - mine is U2410) if I swap the cables around U2413 works as expected
4. While disabling energy saving fixes the issue (as the displays never turn off) this is not a solution temporary or otherwise :(
5. Turning off the monitor and putting it to sleep does fix the issue (sometimes and only temporarily)
6. NVRAM & SMC resets appear to have no effect
7. My mini also does the primary display "flash" before falling in to a coma never to return
On a side not I have noticed that the primary display displays services starting up before the OS has fully booted (Dropbox etc) - so I can see the desktop briefly as a flash then it disappears again, while the actual log in sequence finalises.