I've been working with several instructors who needed to change the general availability date of a quiz for one of several reasons (e.g. unplanned disruption in course schedule, didn't finish teaching course material in time). They have noticed if a student is taking the quiz while they are changing the availability date it doesn't apply to any of those live quiz attempts. We have several large enrollment classes at our university (500 + students) and it is difficult for them to find the time to wait until no students are taking the quiz to change the availability of a live quiz.
I'm proposing that Instructure develop quizzes so any changes made to availability settings retroactively apply to quizzes that are live while those changes are being made.