Whatever is going on between the two of you, it isn’t love. He is holding you hostage by his threat of self-harm. You are scared to leave him. Threats and fears are not the basis for a healthy relationship. Although it has gone on for 5 years, you have not freely chosen to be with him.
I don’t know if you have really “kept him alive” or if he is in the grip of a mental illness or if he perversely likes the game. I do know this: He is not your patient. He is your boyfriend. The terms are different. You are not ethically bound to treat him. The boy you chose when you were only 15 has become a man who is bullying you into staying, even at the price of your schooling and your own mental health. You need to extricate yourself enough so you can think straight.
I suggest that you insist that the two of you see a couples counselor to try to break the cycle of threat, fear, saving, and staying that has been repeating itself for years. If he does have borderline personality disorder, your boyfriend needs to be committed to consistent treatment before he will be ready to be with anyone. You need to take a step away, both for your own health and to stop your part in the cycle. If he won’t honestly engage in treatment, your therapist will be able to help you separate in a way that is healthy for both of you.
As an aside: I don’t know if you are really asexual. You’ve been in an emotionally abusive relationship from a very young age. It could be that your body is telling you this guy isn’t for you by shutting down sexual feelings. You may find that you respond differently to a man who loves and cherishes you fully and without any of this drama.
I wish you well.