Students trying to negotiate away penalties for late submission of coursework I'm teaching a course where coursework is submitted online.
Recently, an important group project assignment was due.
The students are required to submit a project report,
which contains a link to a video produced by the students,
usually uploaded onto a site such as YouTube, Google Drive or Dropbox.
We had announced that for every day that an assignment is late,
students will lose 10% of their score for that assignment.

As you might have predicted,
there were several student groups who submitted their assignments late.
The problem is that some of these students
have sent me e-mails begging me
not to impose the penalty for late submission.
They gave reasons such as:


The original PDF file which we submitted was corrupted,
so after the deadline, we had to submit the PDF again
There were some technical problems with the original video link,
such that it is not possible for the video to be viewed at that link,
so we had to upload a new video and are now sending you the new link
The project was due at 9 PM, and we submitted it at 9 PM
(see our screenshot!) but the system marked it as late


Initially, I told them that
they will be penalized as specified in the policy,
in order to be fair to the students who did submit their work on time.
However, the students continued to say that
I should be more considerate or fair.

In my mind, I want to say to these students,
"Stop wasting my time arguing for marks!"
But this doesn't seem to be
the right way for me to respond to the students.
How should I respond to these students
who keep on asking me not to penalize them
when the penalty is deserved?
Adhere to the guidelines and syllabus you posted. If students can get around consequences of late submission by arguing, you have set a precedent, and they (and future generations of students) will argue again the next time. Don't go there. Consciously cultivate a reputation that pointless arguments don't work with you.

Next time, make it clear that "normal" IT problems like corrupted files or network lag is not your responsibility, and encourage students to upload their work sufficiently early so they won't run afoul of such problems. If possible, allow students to change their submissions, so they can upload whatever they have a week before the deadline, and keep on uploading polished versions, with the last successful submission before the deadline counting for the grade. This is the way most MOOC sites do it.

(Of course, if the university servers went down, you should take this into account.)

This earlier question seems to be similar: How to deal with failing a student? (And I gave the same recommendation there.)