How to deal with exam performances that do not reflect my abilities?
Something seems to be going on that you need to change. I don't have any idea what it is, but it isn't the grade or the "argument" that you need. You say your performance (repeated) isn't representative of your knowledge and abilities. That may be true or not, but something is getting in your way. 

Is it the inability to study properly because you have too many obligations elsewhere? Do you have particularly bad study habits, say assuming you "learn" something by reading it? Do you have particularly bad teachers (also assuming you learn by hearing something once or reading it)? Is it that you had poor teaching in your past and so were never taught the basics? (I learned/memorized my multiplication tables, finally, after finishing a doctorate in mathematics.) Or are exams so stress inducing that you freeze up and can't think normally? 

I'm not one to dismiss any student as not being able to learn mathematics so I won't insult you, but something is blocking you, whether internal or external. You need to find it and change it. It could be as "simple" as you are at the wrong school and they have no way to help you, or no desire to. (Yes, not so simple.) I've had some students who's background was so poor that it was impossible to figure out what I could do for them in the time available. Fortunately, math wasn't their main pursuit so they could be successful elsewhere, but it was very frustrating. 

Each of the possibilities I've mentioned and others, has some way to overcome it. But first you need to self-diagnose the problem. Only then can you attack it.