Thanks for all the comments and suggestions.
As for Volusiano’s question, I have no idea if my ConnectClip is pre-release or non-standard. It is identified as a “ConnecClip 1.1” by the Apple system information app. If I run the firmware option in Genie II (2019.2) under Windows 10 on my iMac (using Bootcamp), it lists the firmware version as 1.13.0 and “Up to date”. The serial number is: 3183430 (reported by Genie and also by the Apple app).
The Oticon rep I spoke to asked specifically if I was using the Sennheiser dongle that was provided with the ConnectClip. I had not been using it - using it got rid of the problem with my iMac.
I agree that OS and driver updates can cause or fix issues. On my work MacBook Pro I sometimes run Windows to allow connection to lab equipment that has only Windows drivers. A windows update made the Apple bluetooth mouse I typically use unavailable. It was paired and connected according to Windows 10 but it did not work. I finally was able to recover use of it many months later by turning off the option to allow the computer to turn off the bluetooth radio to save power (I had not checked that box myself so I assume an update did as the mouse stopped working immediately after an update). That kind of issue might also affect other bluetooth devices/functions …