But I'd always wanted to write a mystery series and Harlequin doesn't do mystery series, so I moved over to Kensington. I may still do more books for Harlequin if they'll have me. There are many reasons for changing a publisher. Even authors of series change publishers from time to time, usually to get a better income or more publicity, or whatever. But many more authors stay with the same publisher for years, as long as the relationship is working out.
Most publishers have an option clause in the author's contract.
This means they get to take first look at the author's second book. It doesn't guarantee they will buy it. And yes, sometimes established authors get rejected. Often it's on the basis of a synopsis, and the author will just come up with another idea. Hope that answers your question.