  The stability of Majorana fermions at the edges of a two-dimensional
topological supercondutor is studied, after quenches to either non-topological
phases or other topological phases. Both instantaneous and slow quenches are
considered. In general, the Majorana modes decay and, in the case of
instantaneous quenches, their revival times scale to infinity as the system
size grows. Considering fast quantum quenches within the same topological
phase, leads, in some cases, to robust edge modes. Quenches to a topological
$Z_2$ phase reveal some robustness of the Majorana fermions. Comparing strong
spin-orbit coupling with weak spin-orbit coupling, it is found that the
Majorana fermions are fairly robust, if the pairing is not aligned with the
spin-orbit Rashba coupling. It is also shown that the Chern number remains
invariant after the quench, until the propagation of the mode along the
transverse direction reaches the middle point, beyond which the Chern number
oscillates between increasing values. In some cases, the time average Chern
number seems to converge to the appropriate value, but often the decay is very
slow. The effect of varying the rate of change in slow quenches is also
analysed. It is found that the defect production is non-universal and does not
follow the Kibble-Zurek scaling with the quench rate, as obtained before for
other systems with topological edge states.
