  The entanglement survival time is defined as the maximum time a system which
is evolving under the action of local Markovian, homogenous in time noise, is
capable to preserve the entanglement it had at the beginning of the temporal
evolution. In this paper we study how this quantity is affected by the
interplay between the coherent preserving and dissipative contributions of the
corresponding dynamical generator. We report the presence of a
counterintuitive, non-monotonic behaviour in such functional, capable of
inducing sudden death of entanglement in models which, in the absence of
unitary driving are capable to sustain entanglement for arbitrarily long times.
