I wonder if it would make more sense to have that tied to when the post notice was created?
For the new and returning user ones it would make no difference as they’re tied to the post creation date, but for custom post notices added manually the timer does seem to be more useful and intuitive starting from the beginning of their ‘life time’. Otherwise you can put something new on and it has the appearance of something old.
Though Lilly’s other idea of making the custom post notices always highlighted is still a better option. 