Well, here's a little mystery. Earlier, I included a graph of a typical water heater burn cycle, including the "dazzled" period of 3 minutes or so. Just today, I saw another graph shape that I had not seen before. It's mostly about the shape of the graphs, not the absolute durations.
I don't really know how much of the shapes of these graphs is due to the intrinsic intensity of the burner flame and how much is due to variation in the illumination sensors. In a normal cycle, the flame stops abruptly. In the weird cycle, the flame seems to taper off gently. The "dazzled" period was about 7 minutes long. It was long enough that I saw a few minutes of "pilot_off" animation on the LEDs. There was no significant wind going on. Before I got down to the basement to check it out, the display had returned to "pilot_on" animation. The next burn cycle, a few hours later, was back to the normal picture.
I'm hoping this is just some unaccounted-for characteristic of how the water heater burns gas and isn't some kind of wearing out of the TSL2591 sensor. The latter would be a bummer since it's only been watching the flame for a few months.