I think I've tracked this down to rsyslogd being updated a few days ago and it not restarting.
So I tried to restart it by hand with /etc/init.d/rsyslogd restart but it failed to stop. So trying to understand why it didn't stop, I tried running start-stop-daemon manually and here's what I see:
# start-stop-daemon -v --stop --retry=TERM/30/KILL/5 --pidfile /var/run/rsyslogd.pid --exec /usr/sbin/rsyslogd
No /usr/sbin/rsyslogd found running; none killed.
# ps ax | grep /usr/sbin/rsyslogd
3401 ? Sl 2:36 /usr/sbin/rsyslogd -c5
9922 pts/3 S+ 0:00 grep -i --color /usr/sbin/rsyslogd
# more /var/run/rsyslogd.pid
3401
Why would start-stop-daemon not be able to find /usr/sbin/rsysogd? It's spelled properly, it's pid is properly in the pid file. (Sure, I can kill it by hand but I really want to know why start-stop-daemon can't kill it because there is probably some underlying problem that needs solving!)