Outlook 2016 users with POP3 accounts that are downloading mail over and over or deleting it from the server when Outlook is set to leave it on the for a period of time, see Outlook 2016 POP Account Problems.
This problem affects Outlook 2010 users with multiple POP3 accounts delivered to one *pst file:
Outlook 2010 is downloading duplicate emails over and over again, but only for my additional accounts, not my default account. I have "Leave a copy of messages on the server" enabled and when I take this setting off, Outlook does not download duplicate emails and works correctly. However I need to leave mail on the server.
This is the result of delivering the secondary accounts to the default data file.
When you leave mail on the server, Outlook needs to keep track of the messages it already downloaded. It uses a hidden message called Mailbox Manager, which it stores in the Inbox. In older versions of Outlook, each POP3 account had it's own Mailbox manager file. In Outlook 2010, the Mailbox manager file is stored in the delivery location for each folder. In Outlook 2010, only one Mailbox manager file exists in a pst when more than one account is delivered. Because one Mailbox Manager is shared between multiple accounts, the last message downloaded for the account is easily lost.
The Mailbox manager file in Outlook 2010 will have a name similar to this:
Outlook Message Manager () (KEY: 47656E6572616C204B657900)
This screenshot is from Outlook 2007, where two accounts are delivered to the same pst file.