HTC Mail:  Move Messages Between Folders, Not Synced on IMAP Server
Sounds like it's just not copying sent messageinto your mailbox at all, only keeping them locally.  I would assume that's just a shortcoming of the app and you'd need to use a different one that supports that feature.  The default client is very basic and buggy.  Have you considered using Gmail?  You can configure it (through the web) to get mail from an IMAP account, and then you could use the Gmail app (which is very good).