  We study the stability of topological crystalline superconductors in the
symmetry class DIIIR and in two-dimensional space when perturbed by quartic
contact interactions. It is known that no less than eight copies of helical
pairs of Majorana edge modes can be gapped out by an appropriate interaction
without spontaneously breaking any one of the protecting symmetries. Hence, the
noninteracting classification $\mathbb{Z}$ reduces to $\mathbb{Z}^{\,}_{8}$
when these interactions are present. It is also known that the stability when
there are less than eight modes can be understood in terms of the presence of
topological obstructions in the low-energy bosonic effective theories, which
prevent opening of a gap. Here, we investigate the stability of the edge
theories with four, two, and one edge modes, respectively. We give an
analytical derivation of the topological term for the first case, because of
which the edge theory remains gapless. For two edge modes, we employ
bosonization methods to derive an effective bosonic action. When gapped, this
bosonic theory is necessarily associated to the spontaneous symmetry breaking
of either one of time-reversal or reflection symmetry whenever translation
symmetry remains on the boundary. For one edge mode, stability is explicitly
established in the Majorana representation of the edge theory.
