Well, first, I do have to wonder why you are doubling the amount of stuff on the user’s harddrive by having both an archive AND a local replica. We usually use one or the other, not both. If the user’s already got a local replica, you can keep all the email there, make sure neither replica is sending or receiving deletions, and set the Space Saver settings to remove older documents from the server.
Your problem may be related to the level of access your user has got and working local-to-local. I’ve found that local-to-local is tricker than it probably needs to be, but maybe that’s because Notes is so server-based. I don’t think it has anything to do with the user’s Notes setup.
Maybe the best thing to do would be to rethink exactly what it is you are trying to do from the beginning. What is the purpose of the local replica? What is the purpose of the archive? Can you combine the functions? Is there another way this can be done?