  We discuss the unitarity bounds on vectors coupled to currents whose
non-conservation is due to mass terms, such as $U(1)_{L_\mu - L_\tau}$. Due to
emission of many final state longitudinally polarized gauge bosons, inclusive
rates grow exponentially fast in energy, leading to constraints that are only
logarithmically dependent on the symmetry breaking mass term. This exponential
growth is unique to Stueckelberg theories and reverts back to polynomial growth
at energies above the mass of the radial mode. As an example, we demonstrate
how the total inelastic cross section of the LHC beats out cosmological bounds
to place the strongest limit on Stueckelberg $U(1)_{L_\mu - L_\tau}$ models for
most masses below a keV. We also present a stronger, but more uncertain, bound
coming from the validity of perturbation theory at the LHC.
