  Marginally stable systems exhibit rich critical mechanical behavior. Such
isostatic assemblies can be driven out of equilibrium by internal activity, but
it remains unclear how the isostatic and critical nature of such systems
affects their non-equilibrium dynamics. Here, we investigate the influence of
the isostatic threshold on the non-equilibrium dynamics of active diluted
spring networks. In our model, heterogeneously distributed active noise sources
drive the system into a non-equilibrium steady state. We quantify the
non-equilibrium dynamics of nearest-neighbor network nodes by the
characteristic cycling frequency $\omega$---a measure of the circulation of the
associated phase space currents. The distribution of these nearest-neighbor
cycling frequencies exhibits critical scaling, which we describe using a
mean-field approach. Overall, our work provides a theoretical approach to
elucidate the role of marginality in active disordered systems.
