The main reason you would want to turn off IS is either for battery life, because it is completely unnecessary or because it is interfering with intended movements. Most mechanical IS systems work by using gyros (fast spinning weights) to stabilize either a key lens assembly or the sensor itself. It takes a fair bit of energy to keep those gyros spinning even if they are near frictionless due to the energy they are expending to keep things stable.
Additionally, they may induce a small amount of vibration themselves as a result of any imperfections in their spin. If you are using a sturdy tripod, then the spinning gyros could actually cause more vibration and thus loss of sharpness than they prevent, so turning them off could help overall.
Finally, gyros don't only stop unintended movement, but also fight against intended camera movements. If you are trying to move the camera around a lot, it will slightly delay your movements and cause your movements to continue slightly after you stop as the system reaches equilibrium again. This lag with the camera fighting against you can be disconcerting and interfere with video or fast action photography. Some IS systems offer a setting to disengage the stabilization in one axis so that you can make horizontal movements without lag, but even then, if you need to make broad vertical and horizontal movements, IS may interfere more than it is worth.