  We investigate the conditions under which periodically driven quantum systems
subject to dissipation exhibit a stable subharmonic response. Noting that
coupling to a bath introduces not only cooling but also noise, we point out
that a system subject to the latter for the entire cycle tends to lose
coherence of the subharmonic oscillations, and thereby the long-time temporal
symmetry breaking. We provide an example of a short-ranged two-dimensional
system which does not suffer from this and therefore displays persistent
subharmonic oscillations stabilised by the dissipation. We also show that this
is fundamentally different from the disordered DTC previously found in closed
systems, both conceptually and in its phenomenology. The framework we develop
here clarifies how fully connected models constitute a special case where
subharmonic oscillations are stable in the thermodynamic limit.
