The sole restaurant on Hong Kong’s southernmost Po Toi Island may close after a half-century serving visiting hikers and boaters lured by the untouched coastline and placid bays.

The owner of Ming Kee Seafood Restaurant, who gave his surname as Leung, said business had declined and he might be forced to close at the end of next month if he could not find a partner.

“Running a restaurant is hard work, and I don’t want to continue any more, and the younger generation is not willing to take over,”...