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If you're not using recent mode, ensure that the option to Leave messages on server in your POP client settings is not checked.
Try enabling recent mode in your POP client by replacing [email protected] in the Username field of your POP client settings with recent:[email protected], and enable Leave messages on server in your POP client settings.
Recent mode fetches the last 30 days of mail, regardless of any other factors. If you don't check Leave messages on server, your messages will be moved to 'Trash' after download.
Try deleting the entry for your Gmail address in your POP client and then re-adding it with all the correct settings. Please note that you may lose your local copy of any previously downloaded Gmail messages.