Why didn't Yukikaze vanish?
If you see episode 9 between 9:54 - 10:03, Kurahashi Miyo says, "Take this. It is the Tsuchimikado family familiar, Yukikaze. Nastsume's father sent it".

This explain why Yukikaze did not vanish 


   but Hokuto vanishes after death of Natsume.


Here is the gif: