Really, when one dies, their spirit leaves their body, meaning they don't really die, they change form.
Thus, due to Afton's multitude of revivals, the line inbetween dead/alive blurs, and the term Zombie becomes irrelavent, meaning that he's reached a form of immortality caused by suffering of many, explaining the murders of children.
Murders cause despair, however, the murders of children causes a great amount of despair. Thus, Afton used the increased concentration of despair and corrupted himself, in the process becoming immortal.
But, like the myth of Achille's, he's got a weakness. He must cause enough despair or death to "recharge" his mandala, or a conduit of spiritual energy. If his Mandala's reserves were to dry up, he would be unable to manifest physically again.
A mandala is a system where a being, a ghost, is trapped, and is pulled toward the next "bus stop" and gains strength at each consecutive point, until it colmunates at the final stop.
