  Following the recent realisation that periodically driven quantum matter can
support new types of spatiotemporal order, now known as discrete time crystals
(DTCs), we consider the stability of this phenomenon. Motivated by its
conceptual importance as well as its experimental relevance we consider the
effect of coupling to an external environment. We use this to argue, both
analytically and numerically, that the DTC in disordered one-dimensional
systems is destroyed at long times by any such natural coupling. This holds
true even in the case where the coupling is such that the system is prevented
from heating up by an external thermal bath.
