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Not strictly true! We're getting the same issue with all our clients at a major corporation with offices around the globe.

Any Mac at this client we upgraded from v6.x.x to 19 (including the latest 19.5) keep dropping off the network and won't refresh or allow a connection

The temporary cure is remove all of the current version and reinstall 6.0, which is very tricky when you can't connect to them remotely.

I'll post a new Bug report as this is a major issue for us

We had exactly the same problem until we bought a cheap  'Dummy HDMI' adaptor by FUERN. That fixed the problem 

BTW we also had an issue with Apple's own RDC not working properly, again the adaptor fixed it.

HDMI dummy plug,Headless Ghost, Display Emulator (Fit Headless-1920x1080 New generation@60Hz)

We're getting problems with some Macs updated to the latest (19.4.25759.7247) version.

No real consistancy as in a few cases they are identical Macs with the same OS

Worked fine on 19.4.25699.7240 and now we get a Black screen but can move the mouse and theoretically control the remote machine.  If we log in via Apple Remote Desktop, then sometimes it allows ScreenConnect to work. 

Makes no sense at all!

No, they were fine under 6.3. I think we reinstalled SC on the few original  machines that had the problem.  

Just upgraded three Macs, 2 x 10.11 and one 10.12 from 6.3 to 6.6. No problems so far.

Will report back when we do the other 30+ machines

This problem still exists in 6.4! Just updated our server and the client, plus a restart and the Mac screen is still blank.