Of course they'll persist. True believers will just move the goalposts. In the late 1990s Bill Kaysing assured people he would recant if an unmanned spacecraft took pictures of the landing sites that showed the artifacts of the mission. Apparently he believed this would never happen in his lifetime, because when just such a mission was imminent, he changed his mind and said nothing would convince him that Apollo had succeeded. If people believe, contrary to all available evidence, that the missions in the 1960s and 1970s were fake, then it's really not hard to keep believing -- again, against all evidence -- that any new set of missions are also fake. Once you've decided to ignore evidence, it doesn't really matter how much of it you ignore, or why.