Maybe a sticking pressure switch? Guessing that power-cycling the pump provides a short-shot of pressure that effectively resets the switch - this may solve itself with repeated resets. Not sure pressure switches are serviceable on the modern ubiquitous water pump such as the Surflow. Maybe try hitting the housing with back of a screwdriver instead of power-cycling.
Wish I had better input.
1970 Willard 36 Sedan Trawler