In order to limit the connections made from a certain IP address, one needs to patch tcpserver, the process which receives all incoming connections and passes them through to QMail. These steps describe how to patch tcpserver on a FreeBSD system, where the QMail SMTP and POP servers are executed with the supervise (svc) daemon.
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).
When trying to start the QMail POP server with the svc command (daemontools), the following error appeared.
The problem got solved by restarting the daemon: