Same issue.
Late 2014 iMac 5k with an external Monoprice 4K display.
AMD Radeon R9 M295X graphics card.
On 10.12.4. I don't know if the problem existed before 10.12.4 as I didn't install Sierra until 10.12.4 was released.
Sometimes just the iMac display fails to come back on. Sometimes both displays fail (in which case I have to remote in to the machine to restart it).
When looking at System Information when this happens the iMac display isn't listed at all. I haven't checked System Information when both displays have failed, but will try to next time. I'd imagine both will be missing.
I've also noticed that when this happens my Bluetooth device(s) disconnect.
Once this happens I've tried switching the port the external display is plugged in to, and tried putting the display to sleep again (it's on a hotkey) while it's not working nothing brings it back up. I've tried resetting PRAM (NVRAM), no luck.
In an effort to help troubleshoot, someone else mentioned some apps they have start from Login. Really, the issue would be any services that stay running all the time. So here is my list, maybe we all have one (or some) in common.
For me these are:
- Little Snitch
- Dropbox
- Divvy
- Moom
- Keyboard Maestro
- SteerMouse
- EvernoteHelper
- TimingHelper
- TransmitMenu