Just four years after opening in a meticulously restored Miami Beach Art Deco building, Apple’s Lincoln Road store is nearly always mobbed, so much so that the company wanted to build a grander, and edgier, glass-enclosed new store down the block.

But that would have meant tearing down a building that, while nearly nondescript in style, sits inside a protected historic district. And when the city’s historic preservation board balked at the idea of demolition, Apple pulled the plug on the proposal.

Now, amid rumors that the famously tight-lipped company is considering leaving the mall, leaving the Beach, or building its larger flagship store across the bay in Miami instead, city leaders, property owners and local merchants who benefit from the store’s allure are in a sweat.

Last week, Mayor Matti Bower sought, and received, assurances from Apple that it doesn’t intend to decamp from Miami Beach. Publicly, Apple remains mum.

“It was unfortunate what happened,’’ Bower said in an interview, while suggesting that Apple had miscalculated in proposing demolition. “I made the overture because they are good people to have in Miami Beach. They bring people here. I said I would help in any way to make them happy, and they assured me they’re going to stay.’’

But in a city that takes pride in its success with balancing strict architectural preservation with often-spectacular new development, the unresolved fate of the Apple store has become a festering sore point.

Some property owners say they fear the preservation board could end up driving off one the world’s most sought-after retailers, or at least diverting to Miami the large clientele that now comes to the Beach for the Apple store and stays to eat, shop or catch a movie on Lincoln Road. Some preservationists, in turn, accuse developers of trying to erode the design safeguards that have helped make South Beach a roaring economic success.

“There’s a healthy tension that must exist between preservation and development, but the board showed a certain amount of inflexibility in a case that required flexibility,’’ said Lincoln Road property owner Lyle Stern, who is redeveloping the nearby historic Lincoln Theater for retailer H&M. “Not every building that has one original cinderblock left has to be saved.’’

But longtime Beach preservationist Herb Sosa, the board’s chairman, contends it was Apple and its development partners, not the board, who wouldn’t compromise.

“We worked on a variety of possible options,’’ said Sosa, adding that he met numerous times with Apple’s designers. “I was under the impression we were in a dialogue. They’re the ones who walked away from the table. Why, I have no idea.’’

An Apple spokeswoman declined to comment.

The fallout from the Apple imbroglio may be still playing out months after the company abruptly withdrew its plan.

Under a measure endorsed by the city’s planning board, two preservation groups, Dade Heritage Trust and Miami Beach Design Preservation League, would be stripped of preservation-board seats — including Sosa’s — which they have long held under Miami Beach city ordinance. The amendment was proposed in October by planning board member Jonathan Fryd, a partner with developer Michael Comras in the proposed new Apple building.