I do use IMAP, with the settings you provide. But since the e-mail doesn't show up in the GMail web interface, I doubt it's linked to IMAP or POP.
I think this is a more important issue, not on the client side, because e-mails are nowhere near to be found, and it is just happening with SOME of the emails sent to me. Is it possible to get official help from Google? If I do not switch to a business edition, can I pay for questions asked to Google?