Hi, I'd like to help you with your question.
It sounds like your boyfriend is trying to control your relationship by ending it whenever he feels like it. This causes you to try to mend the situation, which in turn makes him feel wanted and lets him be the center of attention.
From what you said, it seems that your relationship is very one sided. You support him, are there for him and deal with his behavior, all while trying to carry on with your work and family with no support from him. One sided relationships can drain you pretty quickly and make you feel alone. A relationship needs to be a give and take. Given your boyfriend's physical issues, your relationship may be less of a give and take than most, but for the most part your boyfriend should try to make it more even and provide you with support as well.
Ignoring your texts and refusing to contact you is an immature response. It is always best to ignore this kind of behavior. Paying attention to him while he is acting out is going to reinforce his behavior and he will keep doing it as long as it is effective.
Try backing off when he breaks up with you. Tell him that you are sorry he feels that way but he has the right to end the relationship. Then do not contact him. If he calls you, then wait a while to call him back, maybe a day or so. Try to minimize your response to his behavior. This will help him see that you will not respond to his acting out and the charge he gets out of doing it will then stop.
If your boyfriend keeps doing this to you, you may want to re evaluate the relationship. People who manipulate in this manner usually do not stop and sometimes even get worse. This kind of relationship is going to be a drain on you unless he is willing to see what he is doing and change. You can also suggest therapy if he is willing to go. He needs to see that he has a problem and find better ways to express his feelings.
I hope this has helped you,