How to allow QMail to support more connections per IP

If your Web server uses QMail as mail agent, the problem is due to the fact that QMail has a parameter fixing the max number of connections per IP:
in files:

/etc/courier-imap/pop3d
/etc/courier-imap/imapd
edit the MAXPERIP parameter which is by default fixed to 4 and increase it to your taste. restart the daemon afterwards:
sudo /etc/init.d/courier-imap restart