If you have students needing consistent time extensions, please email us at questhelp@austin.utexas.edu and provide the unique, student's UT eid, and time extension (1.5x, 2x, etc) to be applied to every assignment.
Additionally, Quest provides the ability to provide an extended due date for individual students in order to allow for special cases. Simply go to "Late submits" in the left-hand assignment menu. The drop down will let you select the student to be granted access. Taking this action also automatically pushes back the 'late submitter' availability to view solutions until after they have submitted their assignment. 
While we expect this machinery to behave as set should a student report a problem of not having access when they should after being granted a late submit, please toggle their time forward just by a minute, and then back to the original (extended) time. This resolves the problem the vast majority of time. Any additional help may be received at questhelp@austin.utexas.edu