Securing Archive Audit button in Security Administrator

Does anyone know how to restrict access to the Archive Audit button on the Audit + Logging page in Security Administrator?
We have a sub-admin role that we created and restricts them from everything but creating/modifying users, but they still have access to archive the auditing.
I need to restrict them from having access to this function but I am unable to find any securable object to remove their access away from.
The role has inquiry access to the Server page only and this still allows them to do this.

Anyone know how to secure this button in Security Administrator?