While United claims to have made progress in customer service, it's still clear that more work remains. The airline has long trailed the industry in this regard, a pretty dismal assessment when you figure that United is at the bottom of a business that is famous for poor service. Passengers complain of operational problems and employee attitudes, and the airline reportedly makes little effort to recapture lost customers.

United calls this perception outdated, but the claim isn't nearly as loud as a Canadian and his broken guitar.

Over the summer, singer Dave Carroll vowed to create three YouTube videos about United's breaking his guitar while he changed planes in Chicago's O'Hare airport. The airline balked at paying the $1,200 to repair the instrument. Now, Carroll is two songs into this internet campaign, with combined views of his videos far exceeding five million. In a statement, he indicates that he no longer wants United's money, suggests that they offer it to charity and asks his supporters not to be so hard on Ms. Irlweg.

With such a nice guy saying nice things and defending his "opponent," United was virtually powerless to defend itself. This was made clear when vice president of customer contact centers Barbara Higgins submitted to two interviews with travel writer Christopher Elliott. In the first, she was pleasant, recognized that Carroll had made his point and leaned on the usual "outdated perception" line. In the second, a response to the second video – which should not have been expected, as Carroll announced that he'd be creating three – was considerably more terse, eradicating any goodwill created by the original interview.

The fact that nothing has really changed, of course, doesn't help, either. When asked by Elliott if "the agents handling claims [are] empowered to use their discretion when dealing with grievances such as Carroll's," Higgins replied, "Our agents are empowered to escalate serious concerns that they hear from our guests. We have since provided them with a better way to do that to ensure we can be more responsive to special situations that arise, while also protecting us from the fraud that we see."

Short answer: no.

While United has addressed everything from finances to operations to customer service – at least it says it has – skeptics still abound. In a tight market for air travel, one wonders to what extent an airline can continue to cut without degrading its service (customer and route) and brand.

Yet, United is willing to bet on its success. The airline is now paying employees $100 bonuses for every month it hits the #1 spot on the U.S. Department of Transportation's list of on-time rankings (second place lands each employee a $65 check, as does simply meeting internal goals for on-time service). So far, the company's 42,000 in-the-trenches employees have collected $18 million.

Operations and service need to be balanced against fiscal management, and some are concerned about how much cash the company has. The airline says it has lower debt and lease obligations than other airlines, but analysts eye the company's cash situation with concern. Though it has $2.8 billion on hand, access is restricted by loan and credit card processing covenants. As with everything in the airline industry, perception matters. Other analysts perceive the $2.8 billion in cash as positive, as unrestricted cash is sufficient and the company is likely to be able to raise another $1 billion.

The struggle continues ... not the struggle with Wall Street, customers or anyone else. Rather, United remains engaged in the battle to define and manage its identity.