The hierarchy $h_m^r$ was proposed to classify object types according to their ability to support wait-free implementations of other object types. Recently there has been much research on the question of whether $h_m^r$ is a robust hierarchy. Roughly speaking, a hierarchy is robust if each type is ``stronger'' than any combination of lower level types. For certain models of binding between processes and objects, we prove here that $h_m^r$ is not a robust hierarchy.