Overview
Automatic permissions set up on value list items were not transferring between an export and import. The reason behind this was because there were connections to external databases set up for the value list and they were active for both vaults.
Solution
The resolution here is to make sure the "Disable selected features…:External Connections of object types and value lists" is checked on the Import Content job.
The other solution if there is no connection to external database set up for the value list is to update the automatic permissions name on the value list item, perform the export/import again and all the new permissions should come over.
The root cause here is that the target (import) vault thought it had newer information than the source (export) vault. This caused target vault to ignore any changes made to the source vault content because the target vault thought the target content was more recent.
