94astro, you nailed it. I *held down* Hold, and a silent line came back. I hung up, and the phone's behaving normally again.
Turns out, we've had a new person at that station, who seems to like to lean on the Hold button. Now we know how it's happening.
grider, normally-held calls are recalled or dropped according to the set timers. Apparently, however, exclusively-held calls are not. The CO line eventually disconnects, but the exclusive hold is never recalled, transferred, or cleared. This most recent incident persisted for more than a day and was cleared only just now, thanks to astro's tip.
Thanks guys for the help!