Deleted Messages Re-Appear or Message Remains in the Inbox
1) If you use an IMAP account - particularly Microsoft Exchange over IMAP and you delete a message and it remains in the inbox or re-appears later, you may need to configure Postbox to auto-expunge after every delete.
Open Config Editor.
Type "mail.imap.expunge_after_delete" into the "Filter:" textbox and double click on the row for mail.imap.expunge_after_delete to change the value from false to true.
Then restart Postbox.
2) It could be that your trash folder or deleted messages folder is full. Try emptying these folders to see if this helps.
3) If you go to Preferences | Accounts | <your account> , try configuring the trash to a different folder to see if the problem persists.