Just went through lots of trouble dealing with google apps and imap/pop3 access for a client.   The problem turned out to be that the account was locked.  The fix turned out to be their unlock captcha tool.  There is one for straight gmail located at https://www.google.com/accounts/DisplayUnlockCaptcha and the other for google apps at https://www.google.com/a/[domain.tld]/UnlockCaptcha

I hope this is helpful to someone.

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