Hello Dominique
I have almost eight years administering Moodle, but don't have the PHP/SQL, etc. necessary to start changing background coding; my co-worker gets to deal with that end of things .
It is actually a bigger problem than not being able to duplicate quizzes in one course. I restored the course that seems to be where the problem started and added our test instructor to it. The test instructor can duplicate the quizzes and everything else in the course. The instructor who reported the problem, can 't duplicate anything in the original course or any of her other courses. Based on this, I am thinking that the problem is most likely tied to the user rather than the activity or course.
Worse case scenario, we can create a new account for the instructor, but we would like to know how to prevent this happening in the future and how to fix it, if possible, without creating new accounts.