Let's assume that some small number of airlines continually make small profits (or at least break even). That creates a non-negative balance.
However, let's assume that a number of other airlines are frequently being established and receiving capital investment, before ultimately failing and declaring bankruptcy.
If the losses those airlines represent outweigh the positive balance from our successes, then the industry loses money, despite some players continuing to exist.
To take it further: if you assume people keep making capital investments with capital drawn from other industries, it's possible that the industry continues to exist even whilst no company generates profits in the long term.
In most countries when you go bankrupt, you go out of business. In the US you usually go into Chapter 11. This lets you default on some of your debt, renegotiate contracts, and then come out of bankruptcy stronger than before.
The problem with this is shown with airlines. They would all make a profit if they could just lose some of them. Unfortunately whenever that looks like it might happen, the loser goes into Chapter 11, enjoys a competitive advantage, recovers, and comes out of it stronger. Then someone else goes bankrupt.
http://www.npr.org/2011/11/29/142909836/is-bankruptcy-busine...
That said, consolidation through mergers has happened recently. We will see how that plays out going forward.
Wait, what? How can that be possible? Wouldn't the airlines cease to exist if they never generated profits?