This information is a decade old, but my wife told me that Southwest were the only American airline to make a profit. That could have something to do with it...

EDIT: This recent news article states "Of the five biggest U.S. airline companies, analysts expected only Southwest to report a first-quarter profit":

http://travel.usatoday.com/flights/story/2011/04/Southwest-m...

Some of Southwest's profit comes from fuel price speculation, which could backfire on them much more quickly and easily than their core business:

http://en.wikipedia.org/wiki/Southwest_Airlines#Risk_managem...

From what I understand fuel contract hedging is a pretty standard part of airline business. Obviously hedging has potential to go the other way but it's unlikely to erode profit unless competitors are able to significantly compete on price and steal customers...

Probably for the same reason you don't see Southwest flights on any travel website. Southwest doesn't allow their flights to be booked outside of their website.