At the October meeting, Fryd said he didn’t understand why two groups that often appear before the board should also have two guaranteed seats on it. A board majority concurred without comment, though one dissenter, Henry Stolar, complained that a measure he said represented a “fundamental’’ change in historic preservation in the city was being voted on without debate or public testimony.

The proposed change, part of a broader overhaul of board appointments, is pending before the City Commission.

Bower, a longtime preservationist, calls the change “a bad move’’ that “discredits the person who started it.’’

Fryd strongly insists his amendment was not motivated by the Apple stalemate.

The conflict is playing out amid changing political dynamics on the Beach. Bower was recently reelected to her final two-year term, and some city commissioners have started openly questioning whether the city’s strict historic protections may be stifling new development — a line of thinking that worries Beach preservationists, who fought for years to see them enacted.

“I don’t know how many preservationists are on the commission, and some people can’t wait to start chipping away at our historic districts,’’ Bower said.

But some developers, including Fryd, say the Apple issue could have been resolved with a reasonable path laid out by the city’s own preservation staff.

In a long analysis, preservation director William Cary and his planners concluded that the building Apple wanted to demolish, a bland, rounded one-story building at 1001 Lincoln Rd. that now houses a Gap store, has been so altered over the years that it retains no trace of its 1926 origins, and little architectural distinction.

Cary suggested that the proposed Apple store, and a companion new Gap store, were so superior architecturally that the board could justify tearing down the existing structure — a move he said he did not “lightly’’ propose.

When the preservation board took up Apple’s proposal in June, at least two members seemed to concur with Cary, but a majority, including Sosa, said they could not endorse demolition. Others, while praising Apple’s design — a soaring glass cube that has become the new Apple store prototype — raised questions about its compatibility with neighboring buildings and the pedestrian mall, in particular a squared-off corner at Michigan Avenue and a long wall along that side street.

In the end, the board, without voting, asked Apple to come back with a revised proposal that would have incorporated at least a portion of the existing building. But in September, Apple withdrew its application without explanation.

Robert Wennett, who developed the much-lauded concrete origami parking garage at Lincoln and Alton roads by Swiss superstar firm Herzog & de Meuron, says the board should have bent over backward to accommodate Apple. He said losing it — or effectively blocking the store’s expansion — would hurt not just commerce on Lincoln Road, but city efforts to diversify the South Beach retail economy beyond clubs, clothing shops and dining.

“I understand where the preservationists are coming from. I’m one. They’re afraid that once you open a crack to demolition it becomes a deluge,’’ he said. “But this is one of the most valuable tenants in the world. They provide a lot of jobs. They bring technology and attract the creative class, which is what makes Miami Beach an interesting place for people to live.’’

“It would be short-sighted not to figure out how to allow them to build the kind of store they would like to see.If we allow them to tear that building down, can they build something that would be appropriate on Lincoln Road? Of course they could.’’

But Sosa says Apple could just as easily have adapted the existing building, noting the company’s own website highlights how it has done just that in numerous historic districts around the world, not to mention its present Lincoln Road store.

Demolishing a historic structure — something the preservation board has allowed only rarely, and always in instances where the building is unsalvageable — requires clearing a high hurdle, something Apple didn’t do, he said.

Sosa said the board has been more than willing to compromise with developers, citing Stern’s work on the Lincoln Theater conversion, which after months of negotiations will preserve the historic exterior and portions of the interior, while satisfying H&M’s commercial needs.

“The difference is, they were willing to work with us,’’ Sosa said. “The Historic Preservation board is pro-development. The best historic districts in the world survive because they evolve, and we certainly lead the world in that respect.

“But when you come into a historic district, you gotta give and take. It’s not all about take.’’