Umping close calls at semester's end
You explain to them that in fairness you can't really amend the rules for one without opening that opportunity to all, which is impractical. The semester simply has end at some point. Besides, you say, the deadline for revisions was announced in class and on the syllabus. (I even emailed each student with some strategic suggestions on what they might want to revise weeks ago).
For most, this response is enough. They took their shot or made their case. They aren't happy, but they accept it. A few, however, want to re-litigate the grading standards or at least they want you to explain again why you gave this paper a C when an earlier one got a B. It's a fair question and I always oblige. Still it probably doesn't take the sting away from missing an A by two points.
Perhaps the problem could be solved by cosmetically changing the grading scale. Instead of a 100 point scale, why not have a 1000 or 10,000 point scale? An 89/100 just hurts more than 8,900 out of 10,000. I read about a study in which people were asked to rate the happiness of Olympic athletes on the medal stand. Turns out the silver medalist is seldom as broadly smiling and the bronze medalist. Win the silver and you think I was that close... Win the bronze and you're just happy to be there.