Is there an Alien Base on the Moon? For the past 40 years the Conspiracy Theory rumor mill has spun itself out of orbit with claims this is true, like.. Ever wonder why the Moon landings stopped and why we have not tried to build a Moon Base? It does seem like a better and easier idea than a floating space station with no access to any raw materials or supplies? Conspiracy theorists claim NASA and the Secret service are keeping the story under wraps.