Chrestomanci must always be a nine-lifed enchanter.
An enchanter's spare lives can, with magic, be removed intact and stored elsewhere, to prevent him using them - or accidentally losing them. In World 12A, the technique was pioneered by Gabriel de Witt while he was Chrestomanci, and took several hours of exhausting work for himself and three assistants (including a doctor to monitor the subject's physical health and an astral travel practicioner to keep an eye on the subject's spirit). In Series One, there is a Mage-built weapon that can do the same thing in moments.
Having nine lives does not appear to give one a greatly extended lifespan. If one dies of old age, the new life taking over will make improvements specific to the actual cause of death, but there will not be general rejuvenation: one will still be old, and will die of old age again before very long. In any case, nine-lived enchanters tend to live in interesting times and use up most of their lives in other ways before getting a chance to die of old age.
The number nine is, not coincidentally, also the number of worlds in each Series of the Related Worlds (except Series Eleven, which has its own rules). Although most people have doppelgangers in each world in their series, a nine-lifed enchanter is always unique. It has been suggested that the nine-lifed enchanter contains, concentrated in a single person, all the power that would have been spread out among the nine versions of that person.
Certainly, the nine-lifed enchanter's power is related to the cross-series duplication somehow. Gabriel de Witt mentions in The Lives of Christopher Chant that if a nine-lifed enchanter consistently loses lives in an unusual way - for instance, by going astral travelling with a spare life and letting that life get killed instead of the one he was actually due to lose next - the resultant bending of the natural order causes problems not just in his own world but throughout his series.
There is some doubt about exactly what is meant by a nine-lifed enchanter not having any duplicates. In The Lives of Christopher Chant, Mordecai Roberts says that a nine-lifed person comes about when "all the doubles you might have had ... were never born for some reason", but this is not put to the proof, and in Charmed Life we hear of a nine-lifed enchanter who had at least one double, in the next world along, who died when he was born.