Sometimes a series outgrows the middle-grade category, but more often, readers do.
My library shelves the first book, The Thief, in the middle-grade section. Written in 1996, Turner's twisty tour de force won a Newbery honor, forever anchoring the series as a work of children's literature. The rest of the series is shelved in YA.
Before the American Library Association launched the Printz Award for young adult literature in 2000 (concurrent with the flowering of the YA genre), the Newbery Awards more frequently recognized YA books. In the 21 years since The Thief was published, the series has grown, not just into YA, but to an adult series in terms of complexity, theme, and the age of the characters. The Thief's Gen is recognizably a teen boy, but he's the only character in the series who is. The age of Kamet, the main character of Thick as Thieves, is unspecified, but could easily be over 30. He is no boy. And with the series' publication spanning than two decades, neither are Turner's original fans. A 10-year-old who read The Thief is 31 now.
Not many writers have the luxury of taking five years to write a sequel and finding themselves still with a publisher and fans, but even if authors match the book-a-year pace publishers prefer, readers may age out of a series before the last book is published, even for relatively short series.
Middle-grade readers love series. Series drive the industry, but a flaw in the publishing model is that kids want the whole series now. But while they figuratively "can't wait" for it, often they literally won't. But writers can only write so fast, and publishers have only so much patience for series that shed readers with each concurrent title -- something they tend to do in all age categories, and may do even faster as those readers move on to other interests. Middle-grade may be intended for ages 9 to 12, but readers who start a series in 4th grade may put it behind them before it concludes in 7th.
When do they outgrow it? When do maturing young readers follow a series? JK Rowling's readers assuredly did, following wide-eyed 11-year-old Harry from his middle-grade debut to his grimmer YA conclusion. More often the durability of reader interest depends not just on the progression and maturation of the series, but the orientation of the reader. My 7th grader is still salivating for the next book in Shannon Messenger's Keeper of the Lost Cities series, but a 12-going-on-20 friend who started the series with her can't be bothered.
An advantage of reading middle grade and YA as an adult is that I'll never grow out of it. If it hasn't happened yet, it won't. When Thick as Thieves comes out in paperback, I'm planning to buy the whole set with matching covers. And then I'll read it again.