In my view, it means that some person (i.e., who can gain access to the room that has the disconnects for all units) is on the premises at all times. It does not require a person to be awake 24/7. An apartment manager who lives in the building would satisfy the requirement. If a tenant needs to turn his power back on, he can knock on the manager's front door, wake up the manager, and be given access to the room.
However, if the manager leaves, even for a short run to the grocery store, then some other person must be available, and must have access to the key.