On this morning's episode, it's the day before the big stockholders vote. Rupert is expecting to face an angry mob of stockholders (Variety has the details)...but I suspect he has crunched the numbers and is pretty certain that they won't have the votes to get rid of him.
Despite the illegal activity in England, the unethical (and potentially illegal) activity in Europe, the political brinksmanship in Australia, and the Justice Department investigation in America, it will all come down to this: Rupert and his family control 40% of the stock, and the second biggest investor (a Saudi prince) controls 7% and is on Rupert's side, so he only needs 3% of the other stockholders to support him. The stock price is still in pretty good shape. That fact alone should be able to get him 3% of the vote. That's all he needs.