American Airlines CEO Doug Parker has been busy of late assuring anyone who'd listen that airfares will be going up; indeed that they sooner or later must go up to cover jet fuel prices that are up more than 62% from a year ago.

But nobody seems to be listening.

Instead of fares rising, they're actually continuing a now 5-year downward trend. And there does not appear to be any upcoming opportunity to change that trend line, despite the forecast of the CEO of the world's largest airline.

Travelers paid, on average US$257.88 for their airline tickets in May, down 6.6% from the US$276.06 they paid, on average in May 207 according to new data from the U.S. Department of Labor's seasonally adjusted Consumer Price Index. Worse for the airlines, they're down a full 20% from a peak of US$322.65 in March 2013.

So, at least for now, those hopes for higher fare prices are receding at the very time when Parker - and, in all likelihood, the top officials at the other big U.S. airlines - are growing increasingly anxious for opportunities to push through big price increases.

Parker and his airline compatriots/competitors say they need price hikes because fuel prices have become uncomfortably high. According to the International Air Transport Associations "Jet Fuel Monitor" North American carriers paid an average of US$89.9 a barrel or US$214.10 a gallon for the week ended June 8. That's up 62.2% from one year earlier.