After 1 month Mail App stopped syncing my inbox again. Interestingly enough subfolders were synced but not my inbox and I could not send mails any longer.
No clue what triggered its sudden death. Reinstalling the account did not help. When I created a new user under ML and installed the same mail account with identical settings again, it did work. However still not on the existing user account.
Going back to previous pactches i used for the existing account, I retried this one:
1. first go to Mac Mail Preferences
2. Under Accounts, go to Advanced tab.
3. then from the drop menu "under keep copies of messages for offline viewing"
4. Select: "Don't keep copies of any messages" when the warning message pop-up click ok
5. after you save, close Mail and then re-open it, then the emails you've been trying to delete/move and etc... it will be flushed and the email will start sync normally.
6. remember to go back and put the settings as it was before, then close Mail and re-open.
And yes i revived my maibox again.....for as long as it takes.
Maybe someone can figure out why this works (temporarily).
Menawhile i hope for significant improvements under Mavericks or otherwise i change to outlook i guess.