  We consider the class of quantum stochastic evolutions ($SLH$-models) leading
to a quantum dynamical semigroup over a fixed quantum mechanical system (taken
to be finite-dimensional). We show that if the semigroup is dissipative, that
is, the coupling operators are non-zero, then a dynamical decoupling scheme
based on unitary rotations on the system space cannot suppress decoherence even
in the limit where the period between pulses vanishes. We emphasize the role of
the Fock space dilation used here to construct a quantum stochastic model, as
there are often dilations of the same semigroup using an environmental noise
model of lower level of chaoticity for which dynamical decoupling is effective.
We show that the Chebotarev-Gregoratti Hamiltonian behind a quantum stochastic
evolution is an example of a Hamiltonian dynamics on a joint system-environment
that cannot be dynamically decoupled in this way.
