If all other users are receiving email messages normally and only this particular user has messages delay, then there must be something particular about this user's mail database.
Compare his mail database's size with that of another user. Is this very large? Also, did you recently restart the BES? If yes, then it could potentially worsen the situation as BES will RESCAN all mail databases after a restart. Imagine BES crawling through a 1 GB mail database... (Reference Source: KB-04789 What Is - Restarting BlackBerry Enterprise Server services may cause delays in message delivery
Mail database corruption or huge whitespace could contribute to the issue as well. If mail database size is not the issue, try performing compact or even updall/fixup to be on the safe side as part of the troubleshooting.
RIM has an article describing factors that contribute to message latency (Reference Source: KB-01685 What Is - Factors that contribute to latency
If all above exhausted, then you probably would want to get the RIM tech (if you have TSupport) to review the BES log to see if thread that serves the mail server related to this user is optimized. Sometimes a overloaded/hung thread may cause the delay too.