When I have a few students who run out of time while taking a Canvas quiz I try to go into the moderate tab to reopen it for them & give them additional time (versus making them start completely over with a new attempt). What ends up happening is that I hit reopen and provide additional time but when the student goes to reenter the quiz it closes it again without giving them the additional time.
I know that I can just give an additional attempt but it seems like it should work to hit reopen and provide additional time.
Once a quiz has been submitted in Classic quizzes there is no way to open it back up for students. The only option is to give them another attempt. I know some people when they do this ask their students to just do the questions they didn't have time to complete on that 2nd attempt. As the teacher you will be able to see every attempt in Speedgrader so you can manually combine the results from both to get a correct score. It's not ideal, but it does work.
Using Moderate works to provide additional time before students begin a quiz and you can also provide more time to a quiz in progress, but it can't extend the time of an already submitted quiz.