It’s almost impossible to sue an airline except for violations of federal law and explicit breaches of contracts (and they write the contracts). State contract claims like duties of good faith and fair dealing are pre-empted by the Airline Deregulation Act. This was ruled explicitly on with regard to frequent flyer programs two years ago in Northwest v. Ginsburg.
But consumers can complain to the Department of Transportation (even if DOT has been improperly ignoring legitimate loyalty program complaints). They can also sue in small claims court, where pre-emption issues are unlikely to carry as much weight and where the cost of an appeal is likely greater than whatever relief is obtained.
In the UK, though, airlines will soon be able to charge consumers for certain kinds of complaints.