As a professor, I encourage you to reframe your thoughts: you didn't "miss just enough points to change [your] grade from an A+ to an A"; rather, you earned enough points to rise to an A but not quite enough to rise to an A+. It's amazing how this one detail can result in a huge shift in perspective.
--- Comment by Greg Martin
This comment by Greg Martin
is so good, and so important here, that I want to highlight it here as an answer, and make some broader points about this type of situation. This is somewhat tangential to your specific question, but I will come around to the connection with your question at the end; so please bear with me.
In university-level teaching, it is very common to encounter intelligent ambitious students who have got high grades throughout their schooling and are used to performing at a very high level. Some unfortunately adopt an annoying way of framing their work, where they speak in a way that sets 100% success as the implicit default position, and any derogation from this constitutes "missing out" on points. This is a somewhat natural way that elite students come to speak of these things, since they have always obtained high grades throughout their schooling, and they are sufficiently talented to realistically shoot for 100% on a piece of assessment. In these cases it is somewhat natural for these elite students to frame things as "missing out" on this mark or that mark, since their focus is in weeding out remaining errors in otherwise high-level work. Unfortunately, over time, these students get sloppy with the way they talk about learning, and their language reflects the implicit view that perfect knowledge is the default position for them, and anything less than perfect performance constitutes some aberration, often in need of arguments over grades.
The other thing that is common to encounter in elite students is an implicit reversal of the relationship between learning and grades --- the elite student often considers the formal grade to be of paramount importance, and the learning as a method to increase grades. In reality, learning is of primary importance, and formal grades are merely an imperfect tool to assess the degree of success in that learning. In extreme cases, one occasionally encounters intelligent students who are so concerned with their grades that they allow opportunities for self-reflection and learning to bypass them entirely. Most university lecturers have had at least some experience of a situation where they attempt to impart some broad lesson to the student during a discussion over grades (e.g., pointing out some broad deficiency in their work that is a "soft-skill", which is not easy to quantify), where the student shows no interest in learning from that situation, but is only interested in arguing for a higher mark.
These kinds of attitudes constitute deficiencies in understanding the process of education and assessment; they reverses the true nature of what is going on. For ambitious and intelligent students this generally do not hamper learning too much so long as that learning is done in the confines of a formal course with a fixed scope and assessment structure, and with formal assessment of grades. However, once you come out of that environment, into situations without formal grading, these attitudes tend to stunt learning.
Most PhD programs are focussed primarily on training a student to be able to conduct independent scholarly research. They require students that are proactive in learning, and are hungry for knowledge and improvement outside of their formal courses. Some PhD programs have courses in the early years and others don't have any courses. If coursework is required then you're expected to get good grades in these, but they are merely considered as preparatory work for the real meat of the program --- the main focus of the program is on your ability to learn outside your courses, and to be able to advance your research work under supervision, without getting marks as feedback. Hence, when writing a letter of recommendation for a PhD program, a professor will assess your subject-matter knowledge, as reflected in your grades, but he will also try to assess your ability and willingness to learn independently beyond your formal coursework. If your focus is on making arguments to advance your own grades, to the detriment of self-reflection on your own performance, and opportunities for broader learning, this bodes poorly for your ability to succeed in a graduate research environment, where grades in courses are secondary, and self-driven learning is primary.
I mention these things because they are the background to assessments of a student's ability to engage in self-learning in graduate school. I'm certainly not saying that you have these deficiencies, but please bear in mind that your professor has probably encountered some students with these deficiencies before, and he is trying to figure out if you possess any of these problems yourself. You say in your question that you already made the case for a higher grade and you received an explanation for your marks. Ideally, that would assist you to reflect on how you can improve your work --- not improve your grades, but your work. Anything that reflects a willingness to self-reflect and improve your own work is going to reflect well on you in a letter of recommendation. Anything that reflects an attitude of focus only on formal grades, and a resistance to self-reflection will come out poorly.