Your emails collect on the web server. By default, when Outlook (and other email apps) pick up email from your account, they delete the emails on the server. That prevents the server from filling up and blocking future emails.
Have Outlook remove your emails after 3 days.
Open Outlook.
Go to Tools / Account Settings
Open (Change) the account in question.
Click on More Settings / Advanced.
Select "Leave a copy of the messages on the server" (This is probably already on if you are having problems). Select Remove from server after "3" days.