"I think they're going to have to work very hard to survive," cruise industry analyst and writer Bill Miller told ABC News. "It's going to be difficult because people associate them with two highly publicized mishaps. They may even have to consider rebranding themselves, getting a new name."
Costa is bracing for more bad publicity as the inquiry into the Concordia disaster gets under way in Italy this weekend.
Two Italian newspapers, La Stampa and Il Messagero, are publishing lurid details of alleged drug use, drinking and sexual harassment aboard the Costa Concordia.
"I saw with my own eyes officers taking cocaine – to prove it you would only have had to test them," a nurse identified only as Valentina B reportedly told investigators in pre-trial evidence obtained by the newspapers.
Valentina B says she worked on three Costa cruise ships, "each one worse than the other."
Another woman identified as Mary G is quoted in the documents as saying, "I worked on the Costa Concordia in 2010 for two months. Often the officers and other crew members were drunk. Often we'd say to ourselves, 'If there's an emergency, who is going to save the ship?'"
Mary G also claimed to have been "molested" by a crew member who was high on drugs.
"We operate strict safety and surveillance measures concerning drugs possession onboard our ships," Costa said in a statement. "The possession or trade of narcotics onboard is prohibited. Crew members who possess or use drugs or engage in drug trafficking are submitted to disciplinary provisions and disembarked. Onboard there are checks and preventive actions to discourage such behaviors."
While all of this is damaging to Costa's reputation, not all industry watchers think the brand will disappear.
"No, not the end for Costa, which has operating passenger ships for over 60 years," Douglas Ward, author of the 2012 Berlitz Guide to Cruising & Cruise Ships, said in an email to the Associated Press from a ship off the Australian coast. "But the relentless media spotlight may dilute the brand and perhaps the number of ships in fleet."
With two of Costa's 14 ships out of commission, the company has two new ships ready to launch.
It just finished rebuilding its 1600-passenger NeoRomantica, which is set to sail on its first voyage in the Mediterranean. The company says the cruise is soldout.
And Costa does seem to have learned from the disaster of the Concordia.
While the Bradwells were critical of the way the crew aboard the Costa Allegra behaved in the first hours, they have nothing but praise for Costa's response to the disabled ship.
The Bradwells said after the first few hours chaos aboard the Costa Allegra this week, the crew and the cruise line worked hard to ease the discomfort for passengers as living conditions deteriorated. Costa used helicopters to bring in food, flashlights and bottled water.
"They did what they could do," said Eleanor. "They did the best they could do under the circumstances."