I gave up on Charles Todd's Ian Rutledge series after 5 or 6 books, and only because the author shifted focus from the MC to the current mystery bad guy.
I loved that character, but he got shuffled to the wings.
I gave up on Charlaine Harris' Sookie Stackhouse books after 5 or 6 as well, when the books became slice-of-life, AKA "How many supernatural creatures will Sookie sleep with in this book?"
I'll stick with a series author till they change the focus of the series in a way that no longer grabs me. Their choice, certainly, as it will be mine.
Right now I'm still hooked on CS Harris' Sebastian St. Cyr mysteries. #7 is coming out next month. I still have hope.
I read every single one of Patricia Wentworth's Miss Silver mysteries (40+) because the focus was split evenly between the mystery and her MC + sidekick (both of whom were people I wanted to read more about.
ETA: Kasper, of God, the new ones are dreadful! Book 3 of 4 in the new series basically packed 150 pages of action, plot, and character development into a mere 700 pages. I wanted to gouge my eyes out. I get them from the library, and I plan to get the last one form there next year and read 3 chapers: beginning, middle, and end, just to see how he wrenches some kind of conclusion from this overblown dreck.