Microsoft's Outlook 2016 currently has a bug that deletes emails from your inbox if they're stored on an email server or duplicates emails in your inbox. This issue only affects Outlook 2016 configured to download emails using the POP3 standard. If you're currently experiencing one of these problems, here's a way to work around it while Microsoft tries to figure out a more permanent fix.
According to the Microsoft support page, the issue affects Outlook 2016 version 16.0.6568.2025 configured to use POP3 and have the Leave copy of messages on the Server setting enabled.
You may be experiencing emails being deleted on the server if you have the option Remove from server after [x] days enabled. As for duplicated messages, this can occur if you have the Remove from server after [x] days disabled.
Microsoft is still scratching its head at this one so there's currently no patch available for the issue, but the company has provided instructions on how to work around the problem. One of these is quite simple: configure your email account with IMAP instead of POP3.
This will only work if your email server supports IMAP connections. Alternatively, you can revert back to an earlier version of Office 2016, given the bug only affects version 16.0.6568.2025.
You can find a step-by-step guy on how to work around the problem over at the Microsoft support page.