The partially demolished produce shed at Savannah Highway and Wappoo Road could vanish if a deal doesn’t ripen soon.

Preservationists — many of whom hope to turn the large shed into a farmers market and community gathering spot — had blocked a demolition permit in August, shortly after a crew began knocking it down.

Their efforts delayed the permit only until Charleston County’s Board of Zoning Appeals could decide if it had enough historic significance to require a special exception. The board voted unanimously Monday that it did not.

Charleston Mayor Joe Riley said Tuesday the city still wants to find a way to preserve the shed, an open-air structure that spans more than a football field next to the city’s West Ashley Bikeway.

“I’m hoping that we can work something out. A very fine family owns it,” he said of Jack and Andrea Limehouse, “but I think if we all work hard together, that can be achieved.”

Limehouse Produce Inc. continued to use the building as a distribution site until it moved to North Charleston six years ago.

The city has some leverage because of its potential to relocate part of the bikeway, an old railroad right of way that was converted into a bike and pedestrian path a few decades ago.

“There had been some discussion over the years relocating the Greenway around the building and let it come out onto Wappoo, north of the building,” Riley said. “That would give them a larger site to redevelop and what we think would be a win-win.”

The family, however, has rejected an early conceptual deal, and it’s unclear what the city could do to change their minds.

The family has cited the building’s fragile condition, including termite infestation, and problems with vagrants as justification for tearing it down.

County Planning Director Dan Pennick said the county could write an order later this week that would reinstate the demolition permit.

Monday’s decision to reject the shed as historic shows that the bureaucracy defines what building is historic.

Riley called the early 20th century shed both historic and iconic, and the Historic Charleston Foundation agreed.

The foundation said the shed “was historically used as the Charleston County Wholesale Vegetable Market, a use that is intricately tied to the history of truck farming in the St. Andrews area. This agricultural building is the last of its kind in this area.”

But Brad Sauls, supervisor of Survey, Registration, Grant and Local Government Programs for the State Historic Preservation Office, said he found no record where this property was recorded in a statewide survey of historic properties. And the most recent county survey was done about two decades ago.

Pennick said the county’s definition of what’s historic is “very minimal,” adding his staff would look at how other jurisdictions define the word.

“We’re trying to go back and look at whether maybe we need a better definition.”

Reach Robert Behre at 937-5771.