From a student perspective, managing a lot of classes all at once often allows things to slips through the cracks. It would be an invaluable tool for students to be able to opt in to receive mobile push notifications ahead of the due date.
Maybe one day in advance of an upcoming due date? Perhaps different amounts of time based on the point value of the assignment? Maybe assignments worth more than 100 points warrant a notification a week in advance while assignments worth fewer are notified within a day of the due date.
Or maybe students could even be able to customize their preferences based on their own class grading scale. Maybe a setting like, "Send me a push notification a week in advance of a due date for assignments worth more than ____ points." or "Send me a push notification a day in advance of the due date for assignments worth between ____ and ____ points."