No, we haven't attempted to put a self-sufficient colony of people in Antarctica. Which is not at all the same as "we can't".
Surely it's fair to extrapolate our inability to succeed there into an inability to succeed in a far more harsh and remote locale.
Keep in mind that this isn't to say we could never succeed. Just that this is a very, very difficult problem that we don't even talk about seriously today, let alone study and pursue. Yet everyone just assumes it's somehow trivial and automatic once we decide to try.
What problem did it have that is unsolvable?