If you lose your engines and ditch in the ocean, there's a good chance you will be found using GPS and ELT technology, not to mention any radar or other aircraft that might be active in the area. As far as I understand, very few satellites used for GPS or comms, including ELT, orbit anywhere close to Antarctica. (Not many satellites of any kind are on polar orbits, and an orbit with a high enough inclination to take it that far south would be impractical because it would spend less time over most populated areas.)
If you had to land an aircraft in Antarctica, even if you could find a suitable landing site, you would be every kind of screwed known to man. I think the weather near the poles also gets really bad around wintertime. There are also very few, if any, navigational aids down there, including GPS as mentioned above. Flying over the South Pole just isn't practical from a safety or navigational standpoint.
Military flights do go over the North Pole regularly though, since there's more inhabited land much closer than in Antarctica.