You said you are using POP3 on multiple PCs.

Do I understand correctly that you have your POP3 accounts configured to "Leave email on the server"? i.e. When you download your mail to a PC it stays on the server until you explicitly tell Outlook to Delete it?

I ask, because the next of "The Usual Suspects" would be your Outlook Profile. And the standard test is to create a new Profile. But I need to be sure that any email downloaded by the new Profile is not going to remove the messages from the server, because it will only be a test. We are not going to keep the emails downloaded by that profile. (At least not at first).

If you are OK with this, then:

Create a new Profile.
Use a different PST file than the one used by your Old Profile.
Add only one of your email accounts.
Create an Outlook profile - Microsoft Support

Switch to the New Profile
Switch to another Outlook email profile - Microsoft Support

Check the Send/Receive pages. Got the OK/Cancel buttons? If so:

Add the other email account to the New Profile
Use the same PST file as the first account.
Add an email account to Outlook for Windows - Microsoft Support

Check the Send/Receive pages. Got the OK/Cancel buttons?

Switch back to your Old Profile.