What is the longevity of a three speed ceiling fan switch?
Ok, I don't have an answer about average multi-position switch longevity, but I went ahead and went on my hunch that this was a switch issue and not a fan issue. I found a replacement switch that was almost identical to my broken one and replaced it, and the problem is now solved. I had to look in envy at the other newer switches that use an analog slider to give finer control over the fan speed. But because they had different switch dimensions and because my current fan switch was already in a wall port with a faceplate featuring three switch slots, I went with the part that matched mine.

So, on a sample size of 1, the duration of a wired four-position ceiling fan switch is 14 years.