HIGASHI-OSAKA, Japan — Mitoshi Matsumoto, the most famous 7-Eleven convenience store owner in Japan, wants to do something unthinkable in his 24-hour, 7-day-a-week industry: take a day off.

That’s why, he says, 7-Eleven is trying to put him out of business.

Mr. Matsumoto announced in November his plans to close up shop so he and his two full-time employees could take off New Year’s Day, Japan’s most important holiday, after years of working 14-hour days with few breaks. But on Dec. 20, 7-Eleven’s parent company told him that his store had received more customer complaints than any other in Japan. He had 10 days to address the issues, it said, or the location would be closed.

“They don’t want to let me take New Year’s off. That’s all there is to it,” said Mr. Matsumoto, 57, who has made a name for himself in Japan by publicly defying the company’s demands that franchisees stay open 24 hours. “If they allow me to do this, others will start rising up here and there.”

His decision in February to shorten store hours inspired other franchisees to demand that 7-Eleven allow them to do the same. But the company has been slow to change, he said, so he decided to take New Year’s off in protest.