Once again, an update and reboot stopped sendmail from working by deleting the /etc/init.d/sendmail script. Further, something's broken in makemap, so I can't adjust any alias, access, or other map sendmail needs to work. The way I see it, I can either outsource my e-mail, move to something package-managed (including a different MTA), or continue to deal with these occasional outages.

It seems to be the case that the break occurred on either 23 or 24 May, as there were no messages processed (according to the log files) on 24 May. Apologies if the outage affected you.