Check /var/log/messages, always, and say what version of cPanel is being used on the problematic servers.
I saw this recently as well on someone's server that was running a very outdated version of cPanel. /var/log/messages showed something about a file in /etc/xinetd.d/ not being executable or something. /scripts/upcp resolved the issue automagically, so I didn't bother to investigate further.
Please say which version of cPanel this is happening on.
$ cat /usr/local/cpanel/version
cppop has never been particularly stable. I don't know if cPanel are even developing it any more now that it is deprecated. It's probably a good opportunity to consider migrating over to maildir and courier-imap (pop3) instead.