The Saints, led by their quarterback, Drew Brees, and coached by Sean Payton, finally won a Super Bowl championship after the 2009 season, defeating the Indianapolis Colts, 31-17.

Then came another crisis for the franchise: Bountygate, a scheme in which players were given cash payments to injure opposing players, forcing them out of the game. An N.F.L. inquiry determined in March 2012 that at least one former assistant coach was involved in the arrangement, which began in 2009. The league said that Mr. Benson had directed the team’s general manager, Mickey Loomis, to end the scheme, but “the evidence showed that Mr. Loomis did not carry out Mr. Benson’s directions.”

Mr. Payton was banned for the 2012 season, and the players found to be involved were fined. Mr. Benson apologized to the league.

But he remained upbeat.

“I’m 85 years old; I’ve been in business since I was a teenager practically; I was in grade school and I even had a paper route,” he told The New York Times after Mr. Payton was reinstated in January 2013. “When we had to get out of here to go to San Antonio, we met with the mayor, and the next day we moved to the Alamodome, with offices set up in the basement.”

“Listen, this is all part of life,” he said. “You’ve got to enjoy every day and make the best of it and go forward. That’s what we’re doing.”

There was turmoil anew in January 2015, when Mr. Benson fired his estranged daughter from his first marriage, Renee Benson LeBlanc, and her children, Rita and Ryan LeBlanc, from executive positions with the Saints and Pelicans and said he no longer wanted them to inherit shares in the teams, which they had been given through a family trust. He planned to provide them instead with compensation for the shares based on the teams’ valuation. He said he intended to leave the teams to his third wife, Gayle, whom he had married in 2004.