Re: Constant redoing introductions, celebrity issue?
Fame doesn't cause relationships to disappear. I have not seen it in my game and I have between 20 and 30 played 5 star celebrities. But there is something else that could be doing it that has been part of the game since the beginning. If you don't keep in contact, relationships will slowly fade over time. And when they reach a certain level, the relationship will get so low that it will be as if the two sims never met and you have to meet the sim again. So that may be what you're seeing happening.
I don't play a strict rotation but I have a lot of played sims in the Played Households side of Manage Households, over 500, in my main save so I do see it happen in my game. The game does have a way built in to stop relationships from fading though. You can have your sims work on the Friend of the World aspiration and when you have a sim complete it, you get a reward trait (I forget the name atm) that stops relationship decay for that sim so the relationships for that sim will never fade. I work on that one early for all my sims so I don't have it happen very often.
Hope this helps.