They are not so much gaining influence but gaining notoriety because they are getting the reaction they want. Like this thread. As long as people panic and continue believing that we are going to hell in a handcart then they will continue doing it. As to why they cannot be stopped, they can. But not by continuing down the path that has failed for so long. This article goes a long way to explaining why while this one goes on to explain how ISIS will ultimately not succeed. Seemingly contradictory but both containing elements that need to be considered.