Einstein-Cartan-Sciama-Kibble (ECSK) gravity provides a well-known mechanism for resolving cosmological singularities through spin-torsion repulsion, replacing the Big Bang with a non-singular bounce. Most such bounce scenarios implicitly assume that the global topology of spacetime remains connected throughout the evolution, typically preserving an Einstein-Rosen bridge between the contracting and expanding phases. In this work, we investigate the geometric stability of this assumption. We show that torsion-induced anisotropy generically drives the bounce geometry away from spherical symmetry, promoting the formation of cylindrical throat regions. Using Ricci flow as a diagnostic tool for geometric stability, we demonstrate that such throat geometries correspond to unstable saddle points in the space of metrics and evolve toward finite-time neck-pinch singularities. We argue that while ECSK gravity regularizes curvature invariants, it naturally leads to topological instability rather than a stable connected bounce. The continuation of the solution past the neck-pinch requires topological separation, which we interpret as a controlled geometric transition rather than a physical singularity.