SymptomsHorde is malfunctioning and is not sending emails through IMAP. No useful information can be found in /var/log/psa-horde/psa-horde.log or /usr/local/psa/var/log/maillog.
You may enable debug logging for Horde by changing this value:
grep LOG /etc/psa-webmail/horde/horde/conf.php
$conf['log']['priority'] = PEAR_LOG_ERR;
Do not forget to change it back once you are done monitoring.
See this article:
112316 How to increase verbosity of Courier-IMAP logs