It doesn't sound to me like your mail client could be at fault. After all, it wouldn't be showing messages in your IMAP inbox if they weren't there in your webmail inbox to start off with.
You could verify this by leaving your mail client turned off for a while and only accessing your account through webmail.
If your messages in your IMAP inbox were somehow being "deleted", then they would still show in "All Mail", because, in GMail IMAP, deleting a message only deletes the label, not the message. (Inbox is just a special label in GMail).
It could be a glitch in GMail. If it is, then it would probably sort itself out after a day.
If you've double and triple-checked your settings in webmail, I don't know what else to suggest.
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