In the Great Hunt we learn that novices and accepted sometimes are put out of the White Tower, if they fail in some ways. These girls can channel thus presumably, should live quite long. How can it be that the Aes Sedai didn't know that those girls they put out of the tower live far longer than them? Is this explained somewhere in detail?
There are two nuances that might explain it:
- Channeling, not the ability to channel, without Oath Road = Long Life
- Aes Sedai shun failures, and so do not have much experience with them
Girls who fail the tests and are expelled without becoming Aes Sedai are expected to avoid channeling; any who do so are likely to be hunted down and punished. The Aes Sedai are able to exist because of the strictures they put upon themselves - which make their power predictable and controllable to other secular powers - and they maintain this order by ensuring there are no non-Aes Sedai channellers. So for the vast majority of failed novices, they leave the tower to face a normal lifespan. And, as with women who are stilled or burnt out, Aes Sedai don't really want to know all that much about women who leave the tower.
The Kin, a set of channeling women formed over time from failed novices, were permitted to exist to act as a magnet for runaways, and yet not tracked closely enough to reveal the age of the members of the group. Even the Aes Sedai using the Kin didn't want to look closely enough that they might disprove their theory of a small group of channellers who would soon give up and disappear.
- There was a little evidence
- The Aes Sedai were not inclined to see or consider it
- It wasn't as obvious as it would be if all capable of channeling enjoyed long life.