It's pretty notorious. Airlines routinely go bankrupt and prompt articles like "The Economist explains: Why airlines make such meagre profits"

Despite incredible growth, airlines have not come close to returning the cost of capital, with profit margins of less than 1% on average over that period. In 2012 they made profits of only $4 for every passenger carried. Why has a booming business failed to prosper?

army1987's point is ill-posed and makes little sense in a supply-demand framework - the more interesting question is how much ticket prices would have to rise if fuel got much more expensive, since obviously they would rise & airlines wouldn't simply stop flying entirely.