Same thing here. I have a Garmin Edge 810 SW 6.30 and Garmin connect APP version 4.21.0.19.
When you start the Iphone Garmin Connect App for the first time, the sync happens. The app shows the edge it´s connected with the green circle. The sync icon spins for a while but then goes greyed out and Is not possible click on that icon to manually sync again.
To force sync, I need to close the app, and start again, or, close the bluetooth connection and start again on the edg 810 to force the app connect to the edge.
This is annoyiing because,when i try to send a course or segment to the device, it shows a message that the segment will be available when it completes sync.
Will i have to close and restart the app everytime? Why is not possible manually sync?