Just wanted to follow up.
GoDaddy's IMAP is well known to be very, very broken, and this can come up with any mail app (from Outlook to K9 to Apple Mail).
The way it's broken is that the data it returns is formally fine, but does not represent what's actually there in the user's mailbox. Since the data is formally correct, there is no way to tell that it's wrong, and since a mail server is the only source of information that a mail app has, there is no "workaround" to get the same info from elsewhere.
One example: the number of messages in a folder. GoDaddy's server may return "100" and there are actually "120" (or whatever) messages, so the newest 20 won't be synced -- but there is no other way to know how many there are, other than to ask the server.
http://forums.androidcentral.com/android-4-1-4-2-4-3-jelly-bean/349992-imap-email-k9-native-app-not-showing-complete-inbox-messages-come-disappear.html#post3655945Another example: their server says it supports IMAP IDLE (push mail), and enters push sessions, but doesn't send any changes on them -- again, this is valid, and just means to a mail app that there are no changes in a mailbox (and in reality, you may be getting new messages and seeing them in their web mail).
https://code.google.com/p/k9mail/issues/detail?id=4562Sometimes the data returned by their server isn't even consistent with itself:
https://plus.google.com/+KostyaVasilyev/posts/XyrxcUMVsvuI vaguely recall similar issues with server side search, where their server returns "no matches" or just aborts the connection. Could ask for a debug log, but just don't want to waste your time -- if my code executes a server search command, and the server says "no matches", well, there is no other source of information other than what the server returned.
One thing that might help is to ask GoDaddy support to "resync the account". This is some sort of magic thing that they do (deleting temporary files? rebuilding index files? whatever) that sometimes makes their server work again.