  We calculate the spectrum of the Andreev bound states in a one-dimensional
superconductor with a strong Rashba spin-orbit coupling. We focus on the fate
of the zero-energy Andreev modes in the presence of time reversal
symmetry-breaking perturbations, both at the boundary and in the bulk. It is
shown that the zero modes are destroyed by time reversal symmetry-breaking
fluctuations, even if the mean-field state of the system is time-reversal
invariant and topologically nontrivial.
