Ilovetorrentialrain sorry to hear this.
It sounds quite complicated.
The fact you have been together 8 years and not moved in together. Maybe he is not the right one for you. But he has been with you 8 years and he is unwell and has this appointment.
You asked for advice, here is what I would do, do it or not as you see fit but this is my honest answer.
I would write him a letter apologizing and saying I did not know why I felt it so long to contact back, I realize this must be hurtful. (your own words).
I'd say that I would be popping by in a few days to see him and if he did not want me to do this he needed to ring me for a chat.
I would say I still wanted to be together (if you do) and that I wanted to come with him for his appointment.
I would follow the letter with a visit once I was sure he got the letter (be tempted to pop it trough the door when he was out rather than trust Royal Mail).
Whether you both want to remain 'an item' or not after this bust up, you can still go with him for his medical appointment and be there for him.
If you never argue and then one argument ends an 8 year relationship it really sounds like your relationship was in trouble! Maybe you or he just did not realize it.
Maybe ending it is right but better to end with some degree of closure and a chance to support him - rather than this rather childish ignoring that he is doing (don't tell him you think it is childish!).
If you really want to stay together, fight for him. If you are ready to move on, do so but with closure and ideally an understanding that this is what is happening.
I know it is so crass but I do like Sex and the City and I love Carrie getting her own way here by sheer bloody persistence.