Students trying to negotiate away penalties for late submission of coursework
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.)
How should I respond to these students who keep on asking me not to penalize them when the penalty is deserved?
I would say that your "Stop wasting my time arguing for marks!" just needs a slightly different phrasing. So if students keep bugging you with basically the same unfounded reason to grant some exception, I would finally write something like
"I did consider your inquiry and your arguments throughly. Based on the announced rules, the present facts and the points you raised, I formed the decision that the deduction of 10% does apply in this case. My decision will not be altered after further inquiries."
I feel that it often helps to acknowledge the inquiry and state that you considered the points.
In case you are discussing with the students in person, I would go for "inquiries on grade changes have to made in written form" (paper better than email), see my answer here.
I have tried many methods, to varying degrees of success. Here are some that work.
Check the wording in the syllabus to make sure it's impeccable. For example, "due by 9pm" can be revised to more specific as "due by 9pm, based on the indicated time of submission on [whatever online platform]."
Allow for 15 minutes technical mayhem leniency. If it's due by 9pm and there is a technical issue, and the students failed to notify the instructor about the technical issue by 9:15pm through e-mail, it's considered as late. You may consider adding this term to the syllabus.
Consider a low-risk mock submission. For instance, insert a few smaller assignments or projects into the course so that the students can get to make a pdf, create a video link, and try the submission platform. This would help reducing their anxiety and also provide them a chance to identify possible technical issues.
Slightly evil approach: If you're indeed correct that they were late. And they just want "no late penalty." That's fine. Remember you still have control over bonus. So don't take any penalty, give them what they deserve. It's 10% penalty, which means their score should have been multiplied by 0.9. Now go and divide all other on-time assignment scores by 0.9 to grant other people's an on-time bonus, about 11%. I usually tell them "Now this is technically and validly late. I understand you don't want a late penalty and I am happy to retract that. Do know that I will apply a bonus to other students for being on time." I have also used this at students asking for bonus points or extra credits. I used the same method to them. Thus far, out of about 5 incidences in the last 6 years, no one went for what I proposed. (And it's funny that none of them took it even I switched to absolute grading from relative grading; somehow people cannot accept a scheme that benefit more than just themselves.)
I will not recommend allowing the on-time students another chance to revise for a higher grade. They have done their due diligence to plan their academic life and now would be coerced to spend more time on it. I don't think that's fair.