  Dynamical decoupling is the leading technique to remove unwanted interactions
in a vast range of quantum systems through fast rotations. But what determines
the time-scale of such rotations in order to achieve good decoupling? By
providing an explicit counterexample of a qubit coupled to a charged particle
and magnetic monopole, we show that such time-scales cannot be decided by the
decay profile induced by the noise: even though the system shows a quadratic
decay (a Zeno region revealing non-Markovian noise), it cannot be decoupled by
periodic spin echo pulses, no matter how fast the rotations.
