I too have this problem. Sync on my desktop shows that Sync on my phone is offline.
"Exit" doesn't seem to work. It keeps showing shutdown but it won't exit. I don't restart the phone but I force close the app.
Once I restart the app on the phone the desktop app will see the phone and both immediately start syncing. It will work for some time (days) but then it freezes again.
I agree with the above quote.
Sony Xperia X Compact. Android 8.0, Sync 2.6.3 (8071), battery saving options and sleep disabled
Windows 10, Sync 2.6.3 (1340)