How is breathing involuntary if the muscles that control it are skeletal?
Breathing is controlled by both the Autonomic nervous system and the voluntary nervous system. You see this in instances where our breath rate increases in flight or fight situations glide to the secretion of Adrenaline and also when we intentionally increase the breathing rate when undergoing high levels of activity. This is due to the fact that the involuntary aspect of breathing is controlled by the medulla oblongata and the voluntary aspect s controlled by the cerebral cortex. The fact that it is controlled by skeletal muscles has nothing to do with how it is innervated. For example, Cardiac muscles are innervated by both the hearts own conducting system and by the Autonomic nervous system. 
If you're wondering why the skeletal muscles dont get fatigued, it's because there is a small but significant rest period between each Breathing cycle (inhalation and exhalation). Therefore the skeletal muscles have a rest period. However if a high rate of breathing does occur for a sustained period, they will fatigue and that's why you get cramps after a marathon or a sprint.