Airlines go bankrupt all the time. The upheavals in the industry after 9/11 pushed a number of shaky cases over the brink - Sabena, Swissair, Ansett and Midway are usually quoted (forgive me if I'ver forgotten any).
They might or might not have gone bust anyway. Trading conditions - at least for the Europeans - were very difficult in early 2001.
Several others which have gone under since then will have found the going tougher since 9/11, but the cause-and-effect is less easy to see.