The POP3 server which comes together with QMail had some severe problems: it stopped working after 1 or 2 days. Before that, it worked like a charm, but at some point it just decided to stop accepting incoming calls. The server process didn't die, it was still active and listening on port 110 (according to sockstat -l).
OK, that can happen. But why weren't there any logs describing what happened prior to such state? There was a run script in /var/service/qmail-pop3/log/ in order to log things to /var/log/qmail/pop3, but that directory remained empty all the time.
So this turned out to be a lot of guess work. Sigh...
Looking for the cause why it didn't log at all, I saw the permissions of /var/log/qmail/pop3 were not set right: the qmaill user, used by QMail for logging, was not allowed to write to the pop3 folder. So I adjusted the permissions and POP3 happily started logging. So now it's just waiting for the server to bail out again so I can check the logs.
Except... the POP3 server kept on running. Could it have been that little permission tweak? I don't know why it works, but as long as it works I'm happy. So fingers crossed.