Free volume theories for the dynamics of dense fluids commonly assume (i) that diffusivity increases with average free volume per particle and (ii) that the size distribution of free Volumes can be approximated by that of an equivalent hard-sphere reference system. We use molecular simulations to demonstrate that these assumptions break down when one considers concentrated suspensions of particles with short-range attractions. In these systems, self-diffusivity shows nonmonotonic dependencies on both average free volume and the strength of the interparticle attraction. Moreover, when interparticle attractions are strong, the shape of the free volume distribution is qualitatively different than that of the corresponding hard-sphere reference fluid. We propose a conceptual revision to the traditional free volume perspective that takes into account both the size distribution and the persistence time of the free volumes, and we demonstrate that it can qualitatively capture the disparate behaviors of a model fluid with short-range attractions and its hard-sphere reference fluid.