I’m assuming there’s no change in your title once achieved - even if you no longer have the factors, qualities, or items used to gain PP in the first place?
J-
As long as you reached PP, you stay there. And before that, each of the four capstone qualities can’t be lost once gained.
Can you still be a Patron once you reach those lofty heights?
If so, what may you teach your protegés?
You can teach all four stats. You get a new option "Teaching London", which if I interpret the wiki correctly can teach two stats at a time (either Watchful/Persuasive or Dangerous/Shadowy). There is also an option which increases Making Waves instead.