Subject: failed to authenticate: You are not allowed to route through this server
Not sure about what you mean with “access their database locally from remote location”. But the message looks pretty clear: It says that to access their database, they have to root through some other server (your web server?) which they are not allowed to.
Check the Security tab on the server document(s) to see who is allowed to rout through. If this has emerged just recently, chances are, that someone removed a group from the field Passthru use/Route through or renamed that group in the Domino Directory.