A few thoughts from another college prof who, as an undergrad, was a bitter about "almost" grades a few times himself.
1) I agree with Areyousure - there must be a cut-off. Is 89.5 is an A-, why shouldn't 89.4 or 89.1? Cut-offs are arbitrary but necessary.
2) The syllabus should clarify this issue. I say exactly what is required for each grade: A- requires 90.0 - 93.9; an A requires 94.0 or better. And I state in bold "No rounding up for anyone."
3) Visiting the prof or sending an email might help you. But personally I don't like to be approached like this and certainly won't round up because someone really needs the grade or "really knows the material." How would that be fair to the other students who didn't contact me but earned an "almost" grade? Should I penalize them for accepting my policy at face value and not whining? (For what it's worth, 60% of my students are female but 95% of emails requesting rounding up are from female students.)
4) In the last few years, I've designed my course so there is a subjectively graded assignment (usually a research paper) that is due on the final exam day. If after entering grades from that assignment and the final exam, there is a student that ends up with an intermediate grade for the overall course grade (e.g., 89.x; 83.x, 79.x), I look at the subjectively graded assignment again. In about 75% of cases I "find" another few points so that the student's grade is indeed rounded up and they get the 90.x for the A-. In cases where I really don't think the subjectively graded assignment can be reasonably raised because it simply doesn't warrant adding any points, I will actually dock the assignment a point or two so that it becomes an 88.x. So no student actually sees a final grade that is intermediate. It is either an A- or else clearly a B+. Since adopting this policy, I don't get any more complaints from stressed-out students.