Are you making the Privacy change at the same time as the other edits?
What happens if you just try changing the privacy for the individual activity?
We appreciate the discussion on this topic. We are actively investigating the reports of this issue in order to get it resolved. In the mean time, if you are experiencing this issue, we would recommend that you edit the activity in Garmin Connect online or you can change the Privacy setting for the activity from 'My Connections' to 'Only Me, 'My Groups and Connections', or 'Everyone'.
Currently the issue only occurs if the Privacy setting is set to 'My Connections'.