In my experience with my own DD, and being a coach during her 8U-12U years, my observation was that kids generally need a new bat every year until their growth slows down. There are always some exceptions, but this has been the general trend for most players.
My DD is a pretty big 9-year-old (5', 95 lbs.), and she has gotten a new bat every season she's played. Some of her smaller teammates have tried to keep a bat more than one season, but by the end of the second season they're usually borrowing a bigger bat from a teammate.