Maxym assisted me in finding the correct answer. In his case, the speaker was becoming muted. I had checked for that previously, but he lead me to consider the levels of seemingly unrelated items.

I eventually found that my "Bass Speaker" was set to 0 by default, but is actually mapped to my headphone jack. The level has no effect through the laptop speakers, but it is actually the headphone volume.

It is worth noting that this does not present itself at all in gnome-control-center sound-nua. The only similar setting is "Subwoofer Level" and it is always grayed out.

After running alsamixer, changing the volume of "Bass Speaker" to 100, then closing alsamixer and opening it again, the level was now properly labeled "Headphones", but it still did not appear anywhere in the GTK-based controls.

I also noticed setting the Master volume has no effect when the headphones are plugged in, except that all sound is muted when the level is decreased to 0.

So, should future distraught users stumble across this, check the level of everything in alsamixer; that might work for you too.