The Orleans Parish School Board has gone two years now without a permanent superintendent, and it appears no closer to choosing one than on the day Darryl Kilbert stepped down in 2012.

It’s an impasse that likely has two related causes: competing visions on the board about what type of leader should take over the district, and a persistent divisiveness among board members that is giving potential candidates second thoughts about applying to work for them.

The result is a local school district on autopilot in some ways: The basic teaching and learning continue one school year after another, but some of the bigger questions about the district’s future go unresolved.

“There is a real opportunity to create a first-of-its-kind governance model to go with the type of school system that exists in New Orleans,” said Rayne Martin, a former state education official. “Part of their struggle, in terms of not coming together as a board, is a failure to acknowledge that opportunity, and a lack of vision.”

The type of school system Martin refers to is one made up almost entirely of autonomous charter schools, and the existing governance model is an ad hoc one, with the board in charge of supervising one group of schools and the state-run Recovery School District supervising another.

Advocacy groups like the one Martin runs, Stand for Children, have been waiting to see whether the board will find a superintendent who can help put the new charter system on a more permanent footing, but so far they haven’t seen much progress.

Part of the problem is basic math.

It’s clear now that none of the seven candidates brought in for interviews this year has attracted the five necessary votes on a board that is usually divided 4-to-3. The board went into a lengthy executive session Tuesday evening to discuss two finalists whom members met with last week, but it then voted not to proceed with hiring either of them.

That doesn’t necessarily mean the board won’t eventually choose one of the hopefuls it has already talked with, but it doesn’t bode well for them, either. Board President Nolan Marshall Jr. had gone into Tuesday’s meeting hoping for a decision. But after a long, fraught meeting, he looked grim-faced.

“We’re going to keep working at trying to find the right candidate,” Marshall said, but he acknowledged, “I don’t believe at this point in time that there’s a supermajority that would give the job to either individual that’s applied.”

At the same time, it’s not certain when or whether another crop of hopefuls will be forthcoming. The board interviewed four candidates in March, then another three this month.

Bill Attea, the head of the search firm working for the board, said Tuesday that his company, Hazard, Young, Attea & Associates, will continue accepting résumés until the board makes a final decision, but he added that he isn’t actively vetting or recruiting more individuals at this point.

He attributed the deadlock among board members not to a lack of people to choose from but to a basic conflict over what type of credentials the winning candidate should have.

“The board has never really been able to say exactly what they want,” he said.

It has not been precisely clear what those differences among board members are. The interviews and debates have gone on behind closed doors, and members have stuck with a policy of allowing only Marshall to speak publicly about the search.

What back-and-forth does go on in public has been acrimonious, dividing board members over issues of money and race — factors that have caused friction on the board for decades.

The latest dust-up is over a contract — potentially worth more than $50 million — to build a new Edna Karr High School.

Woodward Design+Build came close to winning the deal in a competitive bid process, with a company called Nolmar Construction serving as a subcontractor and helping Woodward meet the district’s goal for directing a certain percentage of the money to so-called disadvantaged business enterprises, which are typically firms owned by women or minorities.

That brought controversy for two reasons: Nolmar is run by relatives of Marshall, the board president, and it is nearly 50 percent owned by Woodward, an arrangement that struck some as subverting the whole point of the board’s disadvantaged business program.

The district has thrown out Woodward’s bid, but it has nevertheless played into already existing divisions. A minority wing on the board, made up of three African-American members, has been more vocal in pushing for strict enforcement of the board’s DBE goals and more openly sympathetic to activists who have criticized the district for not doing so, even calling for the firing of interim Superintendent Stan Smith.

Last year, Marshall sided with three white board members in deciding to keep Smith on until they find a permanent replacement — and he has drawn the ire of Smith’s critics ever since.

For his part, Smith said, the rolling conflict over the district’s leadership has kept him in the job for longer than he expected and perhaps longer than he would have liked.

Smith will turn 68 in October. “For the past 40 years of my life I’ve been running at full throttle,” he said. “I’d like to relax some.”