I was having a problem with my Gmail Email. It was acting like it was getting deleted until I noticed that emails that I was deleting, were still showing up as unread emails listed under my All Mail Label. I have since fixed this and here is how to do it.
Go to Settings -> Mail, Contacts, Calendars
*if you already had it setup, click that account and turn off the mail setting.
Click Add Account -> Click Gmail -> Setup the account
Now click the Account you setup and turn off Archive Messages.
Now you will notice that you can only sync Mail, Calendars, and Notes.
If you want to sync Contacts too, you need to add another account using the Exchange Option.