How about I'm thinking of failing a student that I teach, who had her final postponed because of a death of an immediate family member, for failing to respond to my emails for the retake
I'm sorry to hear that. Has she tried to make amends by responding to emails yet?
Yes, but I think that it is too late.
If she is out of time to schedule the retake, then you should fail her. She cannot get upset at you for her mistake. You told her when she has to schedule the retake by.
I'm just a bully since I am failing her for her mistake. But I won't let it go since I care about my student's grades.
If you are going to fail the student, you will have to discuss the matter with her parents and explain why. If not, reach out via a different form of communication. Either way, you have to make a solid decision about what you will choose to do.