I wish I had done a few more trial runs before I asked, 'cause now I can't get it to do it again!
Excellent proof of the principal that observing a phenomenon changes it.
This wasn't a labor shortage...I checked, and infrastructure was given first priority, and the stations in question had a full complement of workers. They just quit sending out walkers. I sat and watched using the fire risk overlay, and several of the fire stations sat inert while fire hazard rose and rose until wholesale fires broke out in one neighborhood after another.
Since I can't reproduce it, I can't really expect anyone to explain it for me, except I've been playing several years, and I've seen it happen before, with different types of walkers. I thought I had found an example I could point to, but alas.