Gmail emails "disappearing" from Inbox and Drafts folders in Mail

Someone I know has a Gmail IMAP account in Mail on her Mac with OS X 10.8.4 and again and again emails "disappearing" from the Inbox and Drafts folders.

By "disappearing" I mean that i. e. an incoming email shows up for a short time in the Inbox in the Mailboxes section of Mail (= where the Mail email accounts are) and then disappears there and can only be found in the "[Gmail]/All Mail/INBOX" section that is in the Gmail section at the end of the side bar of Mail for any IMAP account. The same sometimes happens for drafts - they are for a short time visible in the Drafts folder in the Mailboxes section, then disappear and can only be found in the "[Gmail]/Drafts" section further down. I have seen both things happen myself.

There are no rules whatsoever in Mail and also no Filters whatsoever in the Gmail account itself.

I am very much at a loss here and cannot explain this phenomenom - but I know that it must follow some logic law that I don't understand. The whole thing is kind of scary for this person because she is not very computer savvy.

Is there anybody here who can explain what Gmail is doing here and how this can be controlled? Shouldn't it be so that the "upper" Inbox (in Mail) is an exact mirror of the "lower" Inbox (on the Gmail server)?

Thanks a lot! desertman