Does it represent more than 50% of their revenue?
Like I said, it's not a question of popularity of that show. If keeping that show destroys the rest of their business, then they're screwed. And it might be harder to get advertisers if large swathes of people choose to boycott any company that advertises on the show, irrespective of the size of the audience.
Tell me - do you honestly believe that the management of the network haven't weighed up the pros and cons of cancelling the show vs keeping it going? Do you really think they'll completely cancel a show, complete with all of the side-effects of doing so, without first considering whether the show is a net liability in the circumstances first? Do you really think that they're that incompetent?
Except boycotts never actually work.
Actually, generally when boycotts are announced... buisness actually goes up because their name is in the news.