Hi Anthony,
Please try the following steps to narrow down this issue:
1. Check whether the Emails the user didn't receive can be found in Office 365 OWA.
2. Are there any inbox rules result in this issue?
3. Check if you enable archive features on this user's mailbox.
4. If the issue occurs in Outlook, please turn off cache mode, and then test again.
Meanwhile, if you have any updates about this issue, please post them.
Thanks,
Edward Qu