Hey MatsuikoHiroka! Thanks for posting. Just wanted to confirm that I understand correctly. Does the hotkey disappear and you aren’t able to use the hotkey anymore, at random? Could it be happening after you change something else in your settings?
Could you also send me a screenshot of the expanded view of the Hotkey (the same as you attached already but expand the Angle Tool row please, so that I can see more information.
You mentioned you have to reactivate the add-on and rebind the hotkey. Have you tried just rebinding the hotkey?
How did you bind the hotkey? Did you use the button in the Toolshelf on the left? Did you use the Face drop-down menu in Edit mode? Or did you enter the hotkey manually in the User Preferences? Thanks!