The shift cuts represent a sudden, harmful side effect for workers, who at rallies and through social media have urged loyal customers to boycott Market Basket stores in hopes that falling revenues would compel the company’s board of directors to reinstate their former president.

Instead the board — controlled by Arthur S. Demoulas, Arthur T.’s cousin and rival — rejected Arthur T.’s offer Sunday to resume leadership of Market Basket while terms of a possible sale are negotiated.

The ability of Market Basket’s board to hold to its position, while workers bend to economic realities, reveals an imbalance of power in the public struggle for control of the company, said Ted Clark, director of the Center for Family Business at Northeastern University.

“If you’re an hourly employee and you lose a paycheck, that hurts,” Clark said. “But a guy with as much money as Arthur S. can hold out for a long time.”