"updating cache directory" runs forever in Mac Mail plus other ills

Question

Running 10.9.2 on MacMini with 16 gb ram.  Mail version 7.2.  Using SpamSieve
Using my IMAP account...which has 3450 messages in the combined five folders for five different mail accounts.   The folder having the problems below that are folder specific has 2000 messages in it.
Activity shows "Updating cache directory"  "evaluating message x out of 256"  Oddly, the number is usually 256.  It runs through 256 and then starts over again, on and on.  It eventually stops.
It also has great difficulty deleting mail.  I delete it using Erase Deleted Items. Deleted mail is delivered again and again when the app goes to the server.  Often it is Spam that I have deleted after SpamSieve put it in the Spam folder (which is "On my Mac").
I often have the "Can't move mail to x folder".  When I rebuild, it fixes that, but the problem comes back in a day or so.
The appd fails to pickup all the mail unless I Take All Accounts Offline and then go back online.  Even then, it finds more mail if I Quit mail and then immediately restart it. And sometimes when I do that it brings back mail that I recently deleted.
If I use Show Deleted Messages, after I delete, the headers still show up in the Inbox, but themessages are unavailable (which is to be expected).
I have deleted the preference folder in Mail library before and it simply redownloaded everything, but didn't change its behavior.
Wisdom would be appreciated in how to fix these issues.
Thank you, in advance.

Answer 1

I finally had to get FuseMail to "reset the IMAP flags" on their end and everything seemed to resolve itself.