This is weird. Normally, I use Alfred all the time, so when it gets in this weird state, I still reflexively toggle it, curse, then use Spotlight. Turns out that the toggle doesn't permanently break until the process is restarted. This time, I kept Alfred running in its weird state for a bit, in case there was more debugging info I could collect. I kept accidentally toggling it and cursing, but just now, after cursing, I realized that it has started responding to the toggle again. I seems that it might get in this weird state for a limited time, then something happens that causes it to recover. I don't think I did anything unusual to cause the recovery aside from waiting a while.