I think it has to be a relatively drama free year too, in which at least we show upside. We need to soundly beat every team we're expected to and show real competence. Squeezing by inferior competition isn't going to do it. CDC knows, as does every single fan, the signs of a healthy program--execution in all three phases, trouncing inferior opponents, competing squarely against equals and betters, and happiness of players. If we don't see these, I think CDC would be willing to move on, even with a 9 win season.
It seems fairly well established that TH is a dick that not many people like. He certainly doesn't exude the kind of charisma that usually goes along with being at the head of a major FBS program, which, as we all know, is as much politician and leader as it is management and football IQ. I bet CDC recognizes the inherent weakness involved in keeping an unlikeable, technocrat coach at Texas. And if there isn't dramatic improvement, not only in record but in eye-test, we could see a change.