For some years now, I have been giving undergraduate students a 24-hour “grace period” after the formal deadline for papers. If a student is trying to upload a paper five minutes before a deadline and the student loses her internet connection, I don’t need the hassle of making a decision on where to give extensions, and the student doesn’t need the stress of uncontrollable technical problems compounding what she should be doing (writing the paper). So if there are technical problems right before the deadline, no big deal: go to bed, wake up the next morning, and upload the paper during the grace period. No late penalty applies. (Currently, I apply a 20% penalty for papers submitted after the grace period but within the week after the deadline, after which credit is not available. But the specifics do not matter as much as the concept of a short period that functions as a margin of error.)
Some students make a choice to wait until the grace period before finishing the paper (or, in some cases, starting the paper). I make clear to students that I do not know and do not care why a student uploaded the paper in the grace period. But… any problems that arise from a student’s choice to procrastinate are not an excuse any longer.
Having a grace period also allows me to be generous in offering help with drafts without rewarding procrastination: I am happy to comment on drafts submitted before the deadline. But if you view the grace period as an invitation to wait until after the last minute, feedback is no longer available.