The problem:
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: mail for [127.0.0.1]:10024 is using up 20000 of 20000 active queue entries
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: you may need to reduce smtp-amavis connect and helo timeouts
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: so that Postfix quickly skips unavailable hosts
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: you may need to increase the main.cf minimal_backoff_time and maximal_backoff_time
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: so that Postfix wastes less time on undeliverable mail
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: you may need to increase the master.cf smtp-amavis process limit
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: please avoid flushing the whole queue when you have
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: lots of deferred mail, that is bad for performance
Jan 22 17:57:59 server postfix/qmgr[29037]: warning: to turn off these warnings specify: qmgr_clog_warn_time = 0
The solution (found from the postsuper manpage):
> mailq | tail +2 | awk 'BEGIN { RS = "" } / spam@host$/ { print $1 }' | tr -d '*!' | postsuper -d -
/ snip /
postsuper: Deleted: 39819 messages
The cause: I wish I knew…