There's a balance in minor characters. Some will have to come and go as people do in real life. Some should stick around, appear more than once, even grow into major characters.
Too many characters coming and going and unless (a la Doctor Who) you have a good explanation for that, it produces a heavy episodic effect. Most changes in the life of main character(s) will be because of other people, and if the characters never stick around, you can arrange the incidents in any order without much consequence. The stories might have unity of theme, but the series won't.
Unity of plot does not, as some persons think, consist in the unity of the hero. For infinitely various are the incidents in one man's life which cannot be reduced to unity; and so, too, there are many actions of one man out of which we cannot make one action. Hence the error, as it appears, of all poets who have composed a Heracleid, a Theseid, or other poems of the kind. They imagine that as Heracles was one man, the story of Heracles must also be a unity.
All right, a wandering hero might pull it off, on a quest where he learns more and more about how to find what he's after, but there's a reason why most pick up companions.
But continuity in characters has other problems. The first is: Small World. If the policeman is always Paddy O'Neill, or the librarian Agatha Jones, or otherwise people keep repeating, the world starts to get claustrophobically small. I remember royal courts -- normally with hundreds if not thousands of people -- that seem to have only a dozen.
There's also the soap opera problem. More characters, more relationships, more complexity. Some have to shade off to insignificance to keep the focus clear. Life is full of trade-offs.