It is often noticed this behaviour that is apparently seen as an issue occurring intermittently

There are the specific error messages "Unable to locate {table_name} {sys_id} for inbound email processing".

After already checked the referred knowledge article KB0751477, it was found that both the user domain and the case domain are same.

The user that sends the email does not have access to the case.

As the documentation says, there is an impersonation during inbound actions, so the updating suppose to be with the user that corresponds to the email sent.

You can confirm the previous root cause by impersonating the affected user in the target record url:

Check query type and display type business rules on the affected table if ACLs are not restricting the access to the user/role who sent the email. One of the business rules to check is "Case display rule" 

Additionally, you can allow inbound actions to ignore the business rules with the condition !(gs.isInteractive()) when executed by Inbound actions as the community suggests

Always test in subproduction before doing any customisation or changing OOB business rules