The cure for those who have broken mana channels hadn't been created yet.
How could they?
Every single patient that was supposed to be treated, died even before being able to be taken care of by a doctor. They didn't last long because people were either killing themselves to stop the pain that this 'curse' was causing them, or either dying because of the pain itself.
Having broken mana channels was supposed to execrate atrocious pain to the body. Nobody was supposed to move when they have it because the pain would just increase by a lot.
However, Eden wasn't a normal person. He was a vampire.
Thanks to that, he wasn't feeling any sort of pain. But it didn't mean that his body wasn't feeling the pain. Eden's body was tiring more easily than other people because of his mana channels, but he wasn't feeling the pain. So it could be said that in one way, he was quite lucky.