The argument is not valid. Although it may be true, you had two weeks to complete it. That is more than enough time. If you left it to the day it is due, that is irresponsible and your fault. The teacher can’t do anything about it. You left it to the day it was due and now you have to face the consequences.
1. though the argument is valid in itself it leaves room to still ask questions. "why didnt you do it before" "how do i know you're not lying" So, to the teacher this argument might seem like more of an excuse. The student might have had full intentions to complete the project last night, but it just so happened to be the one night the internet was down. now, you can put blame on the students lack on time management skills, but as teachers they should look at the bigger picture. What steps led up to the point where the student only had last night to complete a project. It could be that the student has many other responsibilities to take care of. Due to this the argument should be valid, but not excused.
A better argument would be to explain to the teacher what circumstances the student is facing which caused them to only have that night to complete the project. Instead of just giving a surface lever argument dig deep into the moments leading up to this point. If the student has learning disabilities this could also be a great factor in determining why the student decided to work on the project last minute. For example, with ADHD many people tend to just forget things. In some people ADHD makes it mentally draining to do something they dont want to do especially when timed.