Remote Points scoped to a face have the point created at the centroid of the face and the coordinates of the point are saved in Global coordinates.

After a 45 degree rotation of the part, the face ends up elsewhere, but the remote point does not move. It remains at the original location that was recorded in Global coordinates. You have to repair every remote point to fix this problem.

This is true for implicit remote points such as for a Remote Displacement or Remote Force, not just explicitly created Remote Points.