When using the POP3 protocol to retrieve emails, it is not uncommon for mail clients (like Outlook) to occasionally miss downloading certain emails, or repeatedly download old emails. This can occur due to the mechanism of POP3.

When a mail client connects to the email server to retrieve emails with POP3, it receives a list of emails along with unique identifiers (IDs) assigned by the server. The mail client then maintains a local list or database of these email IDs to track which emails have been downloaded. However, if there are issues such as corruption, misconfiguration, or network interruptions, this tracking mechanism may fail, leading to missed or duplicate downloads.

To troubleshoot this issue:

Firstly, make sure that the POP3 settings configured at your Outlook are accurate. If the settings are correct, proceed to the next step.

To troubleshoot missed downloads in a POP3 configuration, you can attempt to move all downloaded emails from the Inbox folder to another folder (e.g. Read folder) on the webmail. This can help ensure that the email client attempts to re-download those emails during the next POP3 session.
See: How to move emails to other folders on webmail

At times, Outlook may have already downloaded the email but moved it to another folder due to rules that are configured in your account. These rules can automatically sort, move, or delete emails based on certain conditions like sender or subject.
To check if any rules are affecting your emails, go to File > Manage Rules & Alerts in Outlook. For more details, please see: Manage email messages by using rules in Outlook

If emails are not being downloaded or appear missing in Outlook, it is possible that your anti-virus software has quarantined them. This can happen if the email contains URL links, unusual attachments, or content that the anti-virus flags as potentially harmful.
Check the Quarantine Folder in your antivirus software to see if the missing emails are there. Additionally, review the anti-virus settings to ensure emails are not being blocked unnecessarily.

Certain add-ins may interfere with email downloads, causing Outlook to skip messages. Disabling unnecessary add-ins and restarting Outlook can help identify and resolve conflicts.
For more about Outlook add-ins, please see: Use add-ins in Outlook by Microsoft

A corrupted Outlook profile may prevent emails from downloading.
Creating a new profile and reconfiguring the email account can help resolve the issue.
For more details, please visit: Create an Outlook profile by Microsoft

If your Outlook data file (PST) is damaged, it can lead to various issues, including incomplete downloads.
To repair corrupted PST files, you can use scanpst.exe.
For more details, please see: Repair Outlook Data Files (.pst and .ost) by Microsoft

For a more reliable experience, switching to IMAP is a good option. IMAP keeps track of emails and their download status on the server itself, minimizing the risk of missed downloads due to client-side issues.