Question: Why does the Sun rise approximately one minute later each day at this time of the year, but sunset is at the same time for a couple of days in a row?

Answer: The situation you describe occurs as we approach the winter solstice. By contrast, as we approach the summer solstice, sunrise gradually gets earlier, while sunset gradually gets later. The reason for this is that Earth orbits the Sun at an irregular rate. It does not move at a steady pace, but rather speeds up and slows down. Of course, the use of standardized time also is a contributing factor. If people measured time by the Sun (sundials), we would be marking the true movement of Earth relative to the Sun. But that would mean a fluctuating standard of time, which would be much more inconvenient than an apparent anomaly in the sunrise and sunset.