When using a federated repository, is there a way to ensure that my file-based registry will continue to function when a LDAP server is down?

Yes, there is a configuration option that enables the authentication to continue if one or more other registries are down, as long as the ID is found in one of the registries that are still up and functional. The federated repository configuration command to permit this is:
$AdminTask createIdMgrRealm -name ibmRealm -allowOperationIfReposDown true