So this will be a small necro of the thread, but I believe I figured out what is causing the problem.
To be clear - my comparison is between a Mac and a regular Windows 10 PC.
The problem is the Eset Smart Security on the Mac, but only if you use ethernet. If you switch to Wifi - problem is gone. On Windows - also with Eset - the problem never exists.
Fortunately, with more recent firmwares for the Duet - the printer will no longer reboot midprint if I try to connect to it, but it will keep disconnecting all the time.
The workaround for the rebooting is to disable Web protection in Eset when working with Duets (and this happens on all my duet boards and different versions of DWC (even the newest one).