Messages being left on the server and downloaded again often means that the message has some anomaly which leads Thunderbird to think it has not completely downloaded. Usually this gives the effect of blocking all later messages since Thunderbird stalls on the supposedly incomplete download.

If you explicitly delete the repeated message, does it reappear?

It doesn't matter. Once I receive the email, it should be deleted from the server. But then I can go to Outlook.com and the email is still there. Sometimes, I get the same messages 3 times before it finally deletes the messages on the server. I am set to re-check for new mail every 12 minutes. This is not every time. Sometimes it works properly. But it is mighty frustrating. I don;t want to go to IMAP. I want the mail on my computer. No messages are blocked. Everything works properly except for this one defect. I have used TB for several years. Only when I switched my primary server to Outlook.com did this start happening. I also set up TB on a friends computer using Outlook and I get the same results. It does the same thing on that computer. It will intermittently send dupe messages the next time it checks for new email.