Is there a threshold for irreversibility in sheared suspensions?

Recent experiments (Pine \emph{et al.}, Nature 2005) have identified a finite-shear amplitude transition to irreversible motion for the particles in a periodically sheared suspension -- apparent evidence for the finite-shear-amplitude onset of chaotic dynamics. We present an alternative explanation in which the irreversibility persists down to arbitrarily weak shear amplitudes, highlighting the roles played by long-lived clusters of particles in near-contact and by the particular conditions under which the experimental system is prepared.