The Market Basket board of directors were not called for a potential late night meeting Sunday after the company’s shareholders failed to reach an agreement on a deal to sell half of the company to former CEO Arthur T. Demoulas, though talks continued through the weekend.

A source close to the process said Sunday that board members set aside 10 p.m. for a possible phone meeting, though it ultimately was not called. The board is ready to meet when an agreement is reached, however.

It was not clear Sunday evening whether another time has been blocked off, or what issues may be holding up a final deal.

Demoulas last month offered to buy the 50.5 percent of Market Basket owned by his cousin Arthur S. Demoulas and his family for roughly $1.6 billion. The two sides agreed on price, but got hung up on the terms of financing the deal and Arthur T.’s status with the company while a sale is closed. Those issues seem to have been resolved.

Arthur T. on Aug. 3 offered to return immediately as CEO while an agreement was being negotiated. But three members of the board of directors later that week countered with a proposal to bring in Arthur T. and his management team, many of whom had quit in protest or had been fired, to assist in operations, though not in operational control.

Arthur T. rejected that proposal, and said through a spokeswoman that “onerous terms” from Arthur S.’s side held up a solution.

Movement toward a deal accelerated after a five-hour meeting Aug. 17 in Springfield with Massachusetts Gov. Deval Patrick and New Hampshire Gov. Maggie Hassan that included both Arthurs, company board chairman Keith O. Cowan and an attorney representing Arthur S.’s family.

On Friday, Hassan and Patrick said the sides had reached an “agreement in principle” to sell the company to Arthur T., and expressed optimism a deal could be put in writing by Sunday. Arthur T. said through a spokeswoman he saw no reason why a deal could not happen over the weekend.

Market Basket employees have protested and in some cases struck, demanding Arthur T.’s return as CEO. A boycott, aided by a warehouse shutdown that left the stores mostly without perishable groceries, has bled the company of hundreds of millions of dollars since July 18. Many store managers have said their sales are down 90 percent or more.

The board of directors, controlled by Arthur S., on June 23 fired Arthur T. and two of his top lieutenants.

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