She was also dropped from "Charmed" after, IIRC, the second season, for similar reasons. And unlike BH90210, her character was so integral to the plot of the series that the producers must have had a *damned* good reason for booting her, because they had to go through contortions to write around her absence.
Short form: Her character and her two sisters were a trio of modern-day (good) witches, who could only exercise their full power when they joined together on a spell, and invoked "the power of three". After using "the power of three" in almost every episode, the firing of Doherty and the loss of her character would leave a gaping hole in the series -- but apparently they couldn't put up with her anymore and kicked her out anyway. So they had a show about the heroic death of Doherty's character, and then next season the writers bent over backwards to add a plot about the discovery of a "long lost half-sister" that the other sisters never knew about (played by Rose McGowen), and then had her join up as the necessary "third witch".
She must have been a *major* pain to work with, to be worth that much disruption in order to get rid of her.
On 90210, Shannen had the same wonderful relationship with Jennie Garth (the blonde who played her best friend Kelly) that she had with Alyssa Milano. But Jennie Garth knew how to court the fans (or at least she wasn't hopelessly self-destructive) and she won them over. The focus of the third season, Dylan dumping Brenda for Kelly was an ironclad shift in the focus of the show. That henceforth Jennie Garth will be the star, not Shannen Doherty.
Gotta admire that ingenuous solution.