Why is it when a Connect to Mail configuration experiences an issue with an email that causes it to placed to the Inbox with nothing written to the status column?

This is what happens when Intelligent Indexing is configured for a document tray. Intelligent Indexing is overwriting (deleting) the status entry.

For example, the following emails were processed without any attachments. These are the results depending on whether Intelligent Indexing is enabled or not.

Default tray with Intelligent Indexing, in case of an error:

Default tray without Intelligent Indexing, in case of an error:

If we do not want to have these emails in an Intelligent Indexing enabled tray, we should create a tray that is used only for error cases. However, this tray must then be marked as the default tray. 

KBA applicable for both Cloud and On-premise systems.