  We consider recently proposed bouncing cosmological models for which the
Hubble parameter is periodic in time, but the scale factor grows from one cycle
to the next as a mechanism for shedding entropy. Since the scale factor for a
flat universe is equivalent to an overall conformal factor, it has been argued
that this growth corresponds to a physically irrelevant rescaling, and such
bouncing universes can be made perfectly cyclic, extending infinitely into the
past and future. We show that any bouncing universe which uses growth of the
scale factor to dissipate entropy must necessarily be geodesically
past-incomplete, and therefore cannot be truly cyclic in time.
