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Microsoft live.com email use POP3. So e.g. I get new email, I read it and delete. Thunderbird checks for new mails 5 minutes later and redownloads same email I just read 5 minutes ago and deleted it.
E.g. if I delete 20 email messages it redownloads all of them. I have to go to live.com myself manually to delete messages each time to prevent that.
pop3 downloads a separate copy of the email. when you deleted it, you deleted the local copy. Use imap if you want things to sync back to the server, so that what you delete stays deleted – Russell Uhl – 2015-08-17T17:46:06.063
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Using IMAP is one option, as @Russel Uhl already mentioned. As you are using POP3, you can keep using POP3, but then you must change your set-up up to delete the emails from the server once you've downloaded them. (There should be a check box somewhere.) This is common practice for POP3 accounts. Also see this post
– NZD – 2015-08-18T00:04:20.567