Almost 5 months on and I've just been alerted to this thread by another member. In case it is still useful to the OP or to other members in the future, the issue is a table property called SSMATableState with value 'back up copy'.
This property is created in a local Access table when it is first exported using SSMA and the user then accepts the option to link back. The property then prevents the local tables being exported to SSMA again. The solution is to either remove the property or change its value.
For full details about this property and what it does, see my article: https://www.isladogs.co.uk/ssma-table-state/index.html