Money.
Basically, Fox is in business to make money. They make money by selling advertisement space/time. They sell the ads by guaranteeing a certain audience to the companies that purchase the time. If they pander to that particular audience, and tell them what they want to hear, they will be more likely to tune in to Fox programming. Then Fox can show the advertisers that they are reaching the promised target audience, so then the advertisers will buy more time, and give Fox more money, etc., etc. It's just a vicious, self-perpetuating cycle.
As for why Palin is such a cry baby, who knows? Except that she has obviously learned from past experiences that bellyaching gets results. If every time she opens her mouth to squawk about something, she gets some kind of reward for it (a bigger travel budget, better shoes, a VP nomination, media attention, public sympathy, etc., etc.) why on earth would she ever stop?
Hope this helps.