I’ve had my kikr for just over a year. I’ve never had problems with my Zwift click before. My last couple rides on the Trainer have been intervals where the tension is controlled by the profile instead of the click. Currently, if I press the buttons on the click, the number on the screen goes up and down as if I’m changing gears, but the tension doesn’t change. I sent Zwift a message, but they haven’t responded.
Did you get it working? If it’s a Kickr Core, that sounds like this issue: