A 7-Eleven convenience store — that was planning to open up shop in a vacant storefront space on Granite Avenue in the coming months— has pulled out of the deal, according to the building’s owner. The company had come under increased pressure from local elected officials in recent days after their Boston representatives applied for a change of occupancy permit for the space with the city’s Zoning Board last month.

On Tuesday, the owner of the building at 11 Granite Avenue, Thomas Naughton, told the Reporter that the Georgia-based convenience store chain had just terminated their plans to lease the space because they were not likely to win approval to keep the store open 24 hours a day.

Earlier this week, City Councillor-at-Large Stephen Murphy and a representative of Mayor Tom Menino had fired off letters to the corporate offices of 7-Eleven in Georgia, calling for the company to answer questions before a local civic group.

“The particular areas of concern are the hours you are seeking, building design (interior and/or exterior), signage, and potential impact of the traffic that passes through the area,” Murphy stated in the letter, which stresses that he will be “working with my colleagues and the Mayor’s office to address” the community concerns in the “absence of a District 3 Councilor.”

In a nearly identical letter to the 7-Eleven corporate offices, Chris English, who represents Menino’s office in District 3, called it “customary” for new businesses to meet with local civic leaders before setting up shop.

“I would urge you to get in touch with me as soon as possible, so that I may assist in setting up a meeting to discuss the potential move into Adams Corner,” English wrote.

Sean Weir, who heads up the Cedar Grove Civic Association, had told the Reporter this week that he had been frustrated thus far in his attempts to speak to 7-Eleven representatives about their plans for the site. Mainly, Weir said neighbors were concerned about the potential traffic and parking problems that a store could generate at an already congested intersection. He also worries about late-night or overnight hours that could accompany such a chain store.

“We really don’t need it,” Weir said.

The commercial property at 11 Granite Avenue was valued at more than $688,000 last year. It has been at least partially vacant since its main tenant, Hollywood Videos, closed its doors four years ago. The building currently has one tenant, a nail and manicure salon.

Naughton, the president of the realty company that owns the building, said Tuesday that he has no other immediate prospects for leasing the space.

“I’d like to get something the neighborhood would like to see,” Naughton said.