My first question to you would be

Did you lay out the assignment expectations and how the grade would be determined when you gave the assignment?

If the answer is "yes" (and I expect that it is), I would use that as a starting point for explaining to the student why he/she did poorly.

That aside, it seems that either (1) the student didn't understand what was expected (regardless of the question above), and/or (2) the student isn't prepared for the type of work required, and/or (3) the student had a bad day.

It sounds to me like the answer is firmly #2, as repeated attempts to improve the grade hasn't worked. Given that you've already spent a good deal of time with the student, it might be time to have a heart-to-heart discussion and say that it is time to stop thinking about that grade and to move on. Obviously, you need to do this diplomatically, but (as they say), to make an omelet you need to break some eggs, and sometimes a firm and diplomatic "get over it" is appropriate. I would pose the following questions to the student:

1. Do you have a clear set of goals that you are working on for the class?
2. Do you know what other grades are going to be part of the final grade for the class, and do you have a plan for making sure you are ready for each assignment / talk?
3. Do you conduct practice talks with other students in order to get constructive feedback? (if not, you should!)
4. (If the problem is English language skills) Have you sought out on-campus help with your writing or speaking skills? (this is available at many larger universities in the States)

Depending on how much time you are willing to devote to helping the student improve, you could also offer to sit in on any future practice talks to give pointers and feedback. Likewise for written work -- you could offer to pre-read assignments. This is a slippery slope, so tread carefully. You want to avoid having the student see you as an always-available tutor, but there are times when providing such support is just part of the job.

Finally, I would stress to the student that one bad grade does not make or break a student, and it is better to make mistakes while in school than later when they might mean more in the bigger picture. School is about learning, and you learn from mistakes.

This can be tricky.

To answer properly, it is important to know if the student is asking about explanations for his grade or just demanding/requesting a better grade.

The second case seems "easier" to me because then one can just ask for a specific reason why the student thinks, that a higher grade would be appropriate (or just reply that there is no negotiation about grades).

In the first case, when the student asks for explanations, one has to distinguish again: Is the student interested in explanations, to learn from failure and to improve, or to prove that the grading was not appropriate.

Here the first case is easy as soon as you can make sure that the student understands your points. In the second case one could, in principle fall back to the case above: Ask for specific points and don't negotiate about grades. I think that most difficult part is to ensure that you do not have to repeat yourself too often. You could work with written notes for you and/or the student on which you can build for a next discussion. If you see (from the notes) that the discussion is not evolving you can communicate this to the student. If you have the notes of the last session available, and the student raises a point which you have discussed, you can point to the notes and ask what is still remaining about this point. If he repeats the same issue from the last session, answer that there is no negotiation about grades.

Regarding self-esteem and experience of failure, it is important to communicate that science and also learning science if a lot about failure. There is this famous quote from Samuel Beckett:

"Ever tried. Ever failed. No matter. Try again. Fail again. Fail better."

Also, failure in a learning task shall not be related to self-esteem in any way (sometimes hard to accept for students). You can help the student by talking exclusively about his performance in relation to the task he had to do.

I was marking computer programs by hand, which dates this story. I awarded the single worst program 1 point out of 10, which I believe was promised for getting one's name in the correct place. Over half of the lines had elementary syntax errors, which was remarkable because he composed it at a Mac (512!); only the grading was from paper. He thought with only half of the lines clearly, totally wrong he deserved 5/10.

Finally I told him that if I cut off half his body he would be totally dead. This wasn't very nice, but it did stop the complaints.