After Sirius and Buckbeak's escape in *The Prisoner of Azkaban* Snape lets it slip accidentally on purpose that Lupin is a werewolf. Lupin, fearing the parents reaction, offers his resignation, which Dumbledore accepts.

In a similar situation, when Hagrid was exposed as half-giant by the Daily Prophet's reporter, Rita Skeeter, Dumbledore behaved quite differently:

> 
> Dumbledore stood up. “I refuse to accept your resignation, Hagrid,
>  and I expect you back at work on Monday,” he said. “You will join me
>  for breakfast at eight-thirty in the Great Hall. No excuses. Good
>  afternoon to you all.” *~Harry Potter and the Goblet of Fire- Rita Skeeter's Scoop*
> 
> 
> 

Even before, when Draco Malfoy was injured during Hagrid's lesson and his father, Lucius made quite a fuss about his son's injury, Dumbledore stood by his decision to keep Hagrid as a teacher. At some point he also employed Firenze, a centaur, which probably also didn't met with 100% approval from the parents of the students and the more conservative Hogwarts Governors, not to mention the High Inquisitor of Hogwarts. 

Disregarding pressure from prejudiced parents and ministry officials is completely in character for Dumbledore. He was always sympathetic of the situation of people who were derogatorily called 'halfbreeds' by bigots like Umbridge, so I was surprised he'd let go of an excellent DADA teacher who was also an Order member, and who probably saved Harry's life teaching him the patronus charm. There was this little slip of Professor Lupin turning into a werewolf and trying to eat Harry and Hermione, but things like these are really common at Hogwarts.
He also must have known what a miserable existence werewolves led outside of the school. 

So, what could be a good
in-universe explaination why Dumbledore let go of such an excellent DADA teacher?