@blueskate: Please can you confirm if you're attempting to connect a wired or wireless headset? Do you get any error messages when you attempt the connection?
Thanks for confirming. Have you tried using a different pair of wired headphones to see if the same issue occurs? Please also try removing any third-party case or cover from the phone and connect the headphones again. Another important thing is to make sure that the Note 20 is running on the latest software version for maximum stability from: Settings > Software update > Download and install.