Why did Roy Eberhardt's family move so much in the book Hoot by Carl Hiaasen?

The answer to your question can be found on page nine of the novel. The story is told from a third-person point of view, and the narrator states on page nine that Coconut Cove, Florida, is the tenth town that Roy and his family have lived in since he could remember. Roy's father works for the the Department of Justice. His mother explains to Roy that his father is "very good at his job" and that is why they move around so much. She explains that his father is frequently promoted, and promotions are usually followed by a move. The narrator, simulating Roy's thoughts, states, "Apparently that's how the government rewarded good work, by transferring you from one place to another." 

No other details are given about Roy's father's job in the novel. Prior to moving to Coconut Cove, Florida, Roy's family lived in Montana. Roy didn't want to leave Montana and said it was his favorite place where they'd lived.