Somebody did notice. Rather quickly.
Not till it was too late. They didn't notice it had gone off course as soon as it did - only when it failed to land when it was supposed to.
If I was a very powerful person and ran a base in antarctica, and I needed to get some staff there rather quickly because of some emergency, I'd think commandeering a commercial airliner would probably be the way to go. I'd nobble ATC to make sure the only thing that got out was that it had "gone missing". A week or two later I'd then probably also go back and leave a few big bits of metal in the sea to make them think it had gone down there.
Made of tarmac? Look at a map. Look at satellite pictures.
Look at a map?
"Look at a map!" he says!
Me look at a map? what good is a minion, a member of the mere public, such as me looking at a map going to do? You really have just believed the official line hook line and sinker every step of the way and aren't really thinking objectively for yourself at all. If you want to go on believing the world is some kind of utopia that really is exactly as it is presented to be by official channels then carry on but you'll be deluding yourself.
Even if whoever owns the base
wasn't powerful enough to keep satellites away from it in the first place, they've almost certainly got enough clout to keep the pictures off the internet.
If the likes of Microsoft and Google let it be public knowledge that they agree to keep each other's data centres off satellite imagery, then the world elite are certainly not going to go to the trouble of building a base then let it be discovered by commercial mapping satellite.
BTW, I'd rather be conditioned to think the way I do by the media* than be a raving loony, as you are.
Those involved would rather you did as well. Just as well for them that most of the public do, really.