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.