SOUTH PORTLAND — In its last meeting under the helm of outgoing Mayor Jerry Jalbert, the City Council on Monday postponed for a second time a decision on whether to declare property at 29 Willard St. a public nuisance.

On Aug. 4, the council heard public testimony claiming property owner Mary Giggey was burning household trash indoors in her fireplace. In a petition, 15 neighbors said the frequent burning of plastics released “noxious fumes, causing the air quality in our neighborhood to be a major health hazard.”

At that meeting, councilors voted to delay action, allowing Giggey, her neighbors and police the opportunity for better communication and monitoring of the supposed smelly smoke.

But on Monday the issue seemed to disappear into thin air, at least for now, as councilors voted 6-1 to put off any decision on the matter until their Dec. 15 meeting. Councilor Michael Pock was opposed.

City Manager Jim Gailey told the council that city health and fire officials have talked with Giggey, and there have been no further claims of noxious burning. Councilors then debated whether to postpone action or to permanently remove discussion of the complaint from their agenda.

A leader of the neighbors, Ann Thomas, of 45 Willard St., said, “I can now open up my windows,” but urged the council not to close the window on a nuisance declaration.

“The whole neighborhood was up in arms,” she said. “I don’t want this to be set aside so we can’t address it again. I don’t want this to be a dead issue.”

Councilor Tom Blake, who moved for postponement, echoed that caution.

“I want to make sure that if the problem resurfaces, we can jump on it,” he said.

But that may be only a short-term solution, Councilor Linda Cohen said.

“Eventually, we have to put the postponements aside,” said Cohen, who has been nominated by councilors to replace Jalbert as mayor.

Under a 2012 ordinance, owners of nuisance properties can face fines from $100 to $2,500 per day. Thomas previously had told councilors she has tried for six years to stop Giggey’s alleged burning.

Giggey had denied ever burning anything other than wood in her fireplace. She claimed that plastic bottles found in her fireplace during an inspection a year ago had been misplaced by her husband, who was recovering from a stroke.