When you get to the level of working at Mission Control, it should be no surprise that the flight controllers are that beyond dedicated - they also understand the importance of the job as well as the danger to the astronauts so the idea of working overtime where they might make a mistake is anathema to them.
Having been there and knowing that flooding happens every few years in the area, I'm surprised that they don't have backup sites where the controllers can work in the case of a disaster like this. Long term, the Mission Control Center has a lot of required resources, like the training rooms, so keeping everything in one place is the right way to do things.
I'm not sure what the communications (security) requirements are, but I would think there should be the ability to temporarily relocate. Maybe something will be planned after Harvey - although it might be as simple as equipping/converting some rooms as dormitories for the controllers.