  We analyze the rate at which quantum information encoded in zero-energy
Majorana modes is lost in the presence of perturbations. We show that
information can survive for times that scale exponentially with the size of the
chain both in the presence of quenching and time-dependent quadratic dephasing
perturbations, even when the latter have spectral components above the system's
energy gap. The origin of the robust storage, namely the fact that a sudden
quench affects in the same way both parity sectors of the original spectrum, is
discussed, together with the memory performance at finite temperatures and in
the presence of particle exchange with a bath.
