Southwest still has plenty of work to do to repair brand damage and win back consumer loyalty more than two weeks after a technology breakdown forced it to cancel more than 16,700 flights during the busy holiday travel season, a new poll reveals.

Some 45% of U.S. residents have a worse opinion of the airline since before the meltdown, according to a survey conducted by The Harris Poll on behalf of Ad Age. That dissatisfaction rises to 52% among people who have recently traveled with Southwest.

The poll was conducted from Jan. 6 to Jan. 9 among 1,050 U.S adults.

The airline has been the subject of scathing news headlines beginning on Dec. 22 when its scheduling system that assigns crews to flights could not keep up with fluctuations caused by bad winter weather. The situation escalated, with Southwest canceling 62% of its flights on Dec. 27—and things did not start getting back to normal until Dec. 29. Southwest said the disruptions led to an estimated hit of $725 million to $825 million in the fourth quarter, leading the airline to predict a loss for the period.

On Wednesday morning, Southwest had to deal with another disruption that was no fault of its own when U.S. aviation authorities had to ground flights for multiple airlines as result of a failure of an air-traffic technology used by all carriers.

Southwest has attempted to win back customers after the holiday crisis by issuing refunds and reimbursing incidental expenses for those affected. It has also distributed what CEO Bob Jordan described as a “goodwill gesture” of 25,000 Rapid Rewards points to “all customers significantly disrupted,” when he issued a statement of “heartfelt apologies” on Jan. 5. And on Jan. 10, Southwest announced a sale offering $49 fares one-way for travel taking place Jan. 31 to May 17 between select cities.

But consumers want more, according to the poll, with 44% of all respondents and 56% of recent Southwest travelers saying affected travelers should be offered more compensation.

The poll does have a silver lining for Southwest: While 41% of respondents say they are less likely to travel with Southwest now compared to before the mass cancellations, that drops to 34% among Southwest’s recent travelers; and 24% of Southwest passengers actually stated they are more likely to travel with the airline now.  

“It’s never easy for brands to recover from events that result in half of all Americans forming worse opinions of them, and that’s exactly the turbulence that Southwest Airlines must now navigate after its recent meltdown,” said Harris Poll CEO Will Johnson.

But he added: “This challenge is not insurmountable though, at least when you ask Southwest’s own customers, who more often than Americans at large said they are more likely to fly the airline now than before the service outage. This suggests the playbook of taking accountability and making customers whole beyond what is legally required—in addition to helping customers feel confident that the same problem won't leave them in the lurch again—is likely to resonate in building back trust."

Southwest in a statement to Ad Age said: “In addition to our heartfelt apologies, we immediately began an all hands on deck effort to take care of our customers. We are making great progress by processing tens of thousands of refunds and reimbursements a day and will not let up until we have responded to every impacted customer.”

Tim Calkins, a brand consultant and professor of marketing at Northwestern University’s Kellogg School of Management, said “the airline has such a great history of being a friendly, quirky brand that consistently delivered. And this meltdown was profoundly damaging to the Southwest brand.” 

But he added that Southwest’s image will likely improve as time goes by and more people fly the airline under normal circumstances—”and that's going to help Southwest overcome some of the negative experiences.” That gives Southwest an advantage over other brands that experience PR disasters and don't interact with customers on a daily basis, he suggested

An overwhelming majority of poll respondents—77%—agreed with the statement that Southwest “should promote its efforts to make things right with affected customers,” including by using advertising.

GSD&M is Southwest’s longtime lead creative agency.

The airline has so far has communicated its response on its social channels. But its national TV advertising has continued without mentioning the situation—the only spot to get national airtime since Dec. 28 is one called “Souvenirs,” which encourages sports fans to use the airline to follow their favorite teams where they play, according to ad tracking service iSpot.

“I think it's a great time for Southwest to get out there and talk with people and communicate what they might be doing,” said Calkins. “It would be a great time to go buy a Super Bowl ad, to be honest—because Southwest needs to be in front of people with a positive message. And if ever there were a time to invest in your brand, this is the time to do it.”

Asked about its ad plans, Southwest in its statement referred to its mission to provide “friendly, reliable, and low-cost air travel,” adding that “we have a proud 51-year history of doing just that, and we’re confident we'll continue to deliver on this all-important Promise. And we’ll continue to work with our agency partners to deliver on that promise.” But a spokeswoman confirmed that won't include a Super Bowl ad.