An electronic lockbox control system allows visiting agents (such a “showing agents” in a real estate sales situation) to make an appointment to visit a property that is protected by an electronic lockbox, using a time-sensitive authorizing credential that is provided by a central computer; and then, if that visiting agent is delayed because of an earlier appointment, the central computer can automatically create a new time-sensitive authorizing credential that is time-shifted, so that visiting agent can later visit that remote property and obtain access to that lockbox at the later, time-shifted appointment time. Another interested party (e.g., a homeowner) can decline that later, time-shifted appointment. The visiting agent can carry a smart phone with a GPS receiver, and the central computer can use his GPS coordinates to calculate his physical position, and calculate his travel time to the next lockbox location to automatically create the new, time-shifted appointment time.