We restarted the spooler and the backlog is clearing.
So far nothing's been automatically monitoring the phonepost server, but Lisa and Nick will be working on that.
Update: We know why the spooler stopped: the machine was rebooted last night, and the spooler wasn't set to start on boot. That's now fixed. Why the machine rebooted is still a mystery. We're thinking it was a loose power cable while we were working on other machines. Also going to investigate that later.