User blog comment:B214/Volume 22 spoilers/@comment-189.14.202.69-20161016140306/@comment-1359322-20161018062202

A clan is considered extinct only if there's no Pure-blood in them or in their descendant.

For example, if Millicas dies before he has a child with another Pure-blood Devil, then the Gremory will eventually become "extinct" too. That's because there will not be anymore Pure-blooded Devils among the Gremory in time. Rias married Issei, who's not from a Devil origin. So their children aren't considered Pure-blooded Devils, there's mixed heritage in it already.

Reincarnated Devils are called Reincarnated Devils because they do not origin from actual Devils. So all of Issei's children won't be considered Pure-blooded Devils, even the ones with Rias or Ravel.