Same issue here. I use lightdm, but things should be close enough among kdm/gdm/etc.
I had a quick look, what I've found so far is with Synergy 2, synergy-service is runautomatically and it runs synergy-core, which is good. However, at lightdm/gdm, synergy-core can't connect to Xorg due to permission issue.
From Synergy2 log file I can see things like:
[2017-11-25T12:15:01] NOTE: stopped client
[2017-11-25T12:15:05] DEBUG: XOpenDisplay(":0")
[2017-11-25T12:15:05] WARNING: secondary screen unavailable: unable to open screen
[2017-11-25T12:15:05] DEBUG: retry in 60 seconds
[2017-11