[Steve Jordan]

I know it would keep me up! And that's the thing: It is already so hard to hide things on the Moon, it's had numerous flybys of the near and far side, using specialized cameras looking for specific features and elements, that a base would have to be well-camouflaged to stay invisible for so long. So you're talking about a massive conspiracy to bury the inevitable information that would be "discovered" by someone.

We've already seen real-life evidence that conspiracies of that nature don't stay buried for long... all it takes is one intrepid reporter, or one disgruntled employee, and the beans are spilled. It's gotten beyond the suspension of disbelief to expect such a thing to stay hidden, just because the people on the ground wanted it to stay hidden. You'd need a better way to keep it hidden than depending on the usual conspiracy theory.

I think something like this would have to be secret to everyone, even the original Nazis that didn't actually go. You'd need a "purge" after the group left, by agents with a list of people and things to destroy, and no knowledge given as to why, to remove all evidence and memory of the event. (This could lead to an interesting post-war detective story: "Who's killing former Nazi officers and scientists, and why?") If the purge was unsuccessful, the base would have been revealed in the forties.

Then, some very sophisticated camouflage, or else the base would have been discovered by the first dark side of the Moon flybys in the sixties. If you suppose that the Moon Nazis maintained transportation, they may have been visiting Earth often enough to be able to keep abreast of technology, occasionally bring samples home, and use that to improve their camouflage technology and remain hidden until present day.

They would have to use some good disguises, too, in case they were seen, so anyone reporting them would be laughed out of the room. (Maybe if they only send short, thin astronauts, and give them skintight white outfits and big, bulbous helmets with tinted goggles for eyes...)

Even if all of this worked out, chances are they would finally be revealed once civilian/industrial resources were deployed, unsupervised by government, to the Moon. News of a base sighting would get out too fast to be quashed by government sources, and the rabbit would be out of the hat. If the Nazis were going to make a move, it would probably have to be before then.