Any system can stop working. That's all that "offline" means, anyway - it doesn't work. Just because the manual override is, well, manual, doesn't mean jack. It can stop working just like any other system can.
And let's face it, in a freaking STARSHIP, there's not going to be a system that is so manual that it involves turning a crank. You simply don't have things like that on a starship. All Starfleet technology works by computers and pressing buttons - that's simply how it is. Everything is automated. There is no crank to pull. You don't see helm officers steering the ship by turning a wheel - same story here.