We've run into this problem numerous times for special needs students and it causes all kinds of problems for the students, the teacher, etc.
Professors are going in to Moderate Quiz and giving special needs students extra time. It allows them to do this with no issue. The issue is they may have the Quiz set for 60 minutes and have a Start/Until time that is exactly 60 minutes and is set for Everyone in the class. In Moderate Quiz, the professor wants to give the special needs student 90 minutes so they give them an additional 30 minutes in the box. When the special needs student goes to take the exam the Until date/time does not allow the special needs student the 90 minutes they were given in Moderate Quiz because the Start/Until range is only 60 minutes and does not let the extra 30 minutes applied in Moderate occur. That's what keeps happening.
There is no documentation that really says that the Start/Until range needs to accomodate the extra time allocated in Moderate Quiz. Professors could add a different Start/Until range with the +Add option in the Quiz settings for different students that would be in a time range that would take into the account the extra time in Moderate Quiz, but no where does the documentation state this. I think at least the documentation needs to be updated to reflect this situation, but having additional time added in Moderate Quiz for certain students should over-ride the Start/Until range for a Quiz and not the other way around.