I've witnessed two demotions at my squadron, one of which was probationary and the other he was discharged from the Corps. You must be 'consistently poor mannered, behaved or consistently lacking in general leadership skills' to be demoted, even so you would be placed on some form of probationary period.
Get the reasonings for your 'threat of demotion', and write them down; If you feel that the reasoning is just, then accept it. Otherwise I'd recommend contacting somebody within your Wing- your best chances being the Wing Warrant Officer, and make him/her aware of this (preferably by email, so you have record). If your CO lies through her teeth to the wing, then you've probably lost the battle if they believe her!
Good luck.