Hi Dave,
Based on your description, I understand that your Office 365 mailbox has stopped receiving email.
Before moving on, I would like to confirm more information.
1) Could you check size of the mailbox. If it's approach 25G, it might be causes for this issue.
2) Check whether other internal users (users that are in the same Office 365 tenant) encounter the same issue.
3) Check whether internal emails (email between the users that are in the same Office 365 tenant) work well.
4) Please get the full NDR and post it in the forum.
Meanwhile, if you have an enterprise subscription of Office 365, you can also refer to steps below to check the rules/filters in FOPE for your organization.
1. Logon MOP with the global administrator.
2. Choose Admin > Exchange Online, Click Manage.
3. Choose Mail Control. You should be able to see the hyper link of FOPE.
You can refer to this link: technet.microsoft.com/.../ff715254.aspx
Thanks,
Jerry Cen