We explore the persistence of the alignment of brightest cluster galaxies (BCGs) with their local environment. We find that a significant fraction of BCGs do not coincide with the centroid of the X-ray gas distribution and/or show peculiar velocities (they are not at rest with respect to the cluster mean). Despite this, we find that BCGs are generally aligned with the cluster mass distribution even when they have significant offsets from the X-ray centre and significant peculiar velocities. The large offsets are not consistent with simple theoretical models. To account for these observations BCGs must undergo mergers preferentially along their major axis, the main infall direction. Such BCGs may be oscillating within the cluster potential after having been displaced by mergers or collisions, or the dark matter halo itself may not yet be relaxed.