Wild guess - something in there has a timer that gets lonely after 7 days and tries to find a friend. It keeps feeling like a smart device gone bad. A simple timer IC could get close to this accuracy; but it feels more like smart. Do you share a power transformer with any other houses. If so, do they have a line based control system? Check it out.
Still a possibility of the power company. Tech support accessible to any mere human in the US tends to not be able to find their ass with both hands in a brightly lit room. Particularly if they say their name is Bob and the accent is too thick to understand. Don't dismiss that possibility. Do you have any appliances equipped to be controlled by the power company to shed load?