Cost leadership means you are using your uniquely low costs to beat competitors, do well and make good profits. But what would happen if one of your competitors discovered a way of making the product using a new process that meant their costs were even lower than yours. How could you respond (assuming their method is protected by patents)?
There is little merit in being the second cheapest – the fall-back position: the cost leader will win.
So, you have no way of easily fighting the competitor’s dominance.