Phoenixes were known to be immortal. I mean--they are, but things have changed. Descandants of phoenixes, who were much more human-like than their ancestors, die much more easily, by a death curse. At a specific age, the curse kills them, but ofcourse, they rebirth after a century. In each phoenixes bloodline (there are few left), the death curse activation age closes to their extinction at every death. When the phoenixes bloodline is depleted, that is the end of the bloodline. So, each phoenix lives until the death curse kills them, and rebirth after a century.