have been having similar problems with my mail accounts for some time now with the Mes and has turned into one of my biggest issues with the phone! No notifications, spotty service, late mail, and at times no mail at all! Have worked on this for some time with no cure, so I gave up on the stock client and try third party, downloaded K-9 mail to see if this would work better...simply put, HUGE IMPROVEMENT! Much nicer UI, fast mail download, no delete lag AND the mail is actually delivered to the inbox consistently!
Not sure if this is the best mail client available but it has a unified inbox w/limited support for outlook...works great with my pop3 and gmail accounts
Cheers