Important: Before you do anything else, please open a support ticket.
Sometimes the background service can get into a bad state. This is most commonly caused by either sleep/resume, a change in IP address, or just random bad luck, but other factors can affect it as well. This is a known bug and we're urgently working on a fix for this problem.
In the meantime, please could you open the Synergy config app and press the key combination Shift+F5 on both computers. This will restart the service, and you'll have to click Retry afterward. You may need to repeat the key combination it a few times, but if that doesn't work, you can also try restarting your computers. This should solve the problem, but if not, please send me your most recent log links so we can try some more solutions.