For its part, American says that ticket sales have not been hurt after the break with the travel companies, which has now lasted about three weeks.
Airfare experts say the ongoing battle will mean more work for passengers looking for the cheapest flights.
"The move does make things a bit more difficult for consumers in terms of comparison shopping, since they will have to remember to search American separately if using Orbitz," said Anne Banas, executive editor of the travel website SmarterTravel. "However, my advice would be to use a meta-search engine like Bing Travel or Kayak that searches multiple sites -- including Orbitz and American -- at the same time."
At the same time, Google is trying to buy the airfare search software company ITA for $700 million, an acquisition that is being reviewed by the Justice Department for possible anti-trust violations.
While ITA is not a household name, it has some of the most powerful airfare search technologies, often sold to third parties. Google dominates the overall search market and has transformed areas ? think of Google shopping ? that it has entered. Competitors say they fear that if Google buys ITA, it would control airfare searches and give preferential treatment to the highest-bidding advertiser.
"Google buying ITA would be a very bad deal for consumers," said George Hobica, president of airfarewatchdog.com, which refers ticket buyers to several sites including Orbitz and Expedia.
So why would American and Delta make their tickets harder to find? Money.
For instance, consider a $160 Delta Air Lines ticket from Boston to Orlando, stopping in Atlanta each way. If that ticket were purchased on Orbitz, Delta would have to pay $16 -- or 10 percent of that ticket price -- to the booking site. If that same ticket was purchased on Delta.com, the airline would get to keep every cent of the $160 airfare.
"They are trying to flex their muscles and control their distribution costs," said Graeme Wallace, chief technology officer of FareCompare.com.
Southwest Airlines -- which like American is based in Dallas -- has long resisted allowing others to sell its inventory. Mann estimates that roughly 80 percent of Southwest's tickets are sold directly by the airline. It used to be higher, but the airline opened up some of its higher-cost tickets to corporate travel agents to woo business travelers.
Traditional network carriers, like American and Delta, only sell 20 to 30 percent of tickets directly through their websites.
"This frustrates them," Mann said.
Orbitz -- which had unsuccessfully gone to court to block American -- calls its departure "unfortunate" and said the airline accounted for about 5 percent of its overall sales.
While American's move isn't likely to have an immediate impact on ticket prices, other airlines are now likely to review their own deals with third-party booking sites.