  We analyze the quantum dynamics of periodically driven, disordered systems in
the presence of long-range interactions. Focusing on the stability of discrete
time crystalline (DTC) order in such systems, we use a perturbative procedure
to evaluate its lifetime. For 3D systems with dipolar interactions, we show
that the corresponding decay is parametrically slow, implying that robust,
long-lived DTC order can be obtained. We further predict a sharp crossover from
the stable DTC regime into a regime where DTC order is lost, reminiscent of a
phase transition. These results are in good agreement with the recent
experiments utilizing a dense, dipolar spin ensemble in diamond [Nature 543,
221-225 (2017)]. They demonstrate the existence of a novel, critical DTC regime
that is stabilized not by many-body localization but rather by slow, critical
dynamics. Our analysis shows that the DTC response can be used as a sensitive
probe of nonequilibrium quantum matter.
