The increasing densification of small-cell networks substantially expands cable-based backhaul infrastructure, creating heightened vulnerability to cable link failures. This paper proposes a reconfigurable intelligent surface (RIS)-assisted backup framework that exploits a key insight: during backhaul cable failures, base station (BS) radio components remain functional, enabling wireless backhaul traffic redistribution. Our framework maintains network connectivity by redistributing disconnected BS backhaul traffic to neighboring BSs through RIS-assisted wireless links. To maximize survivability across varying traffic conditions, we formulate a joint optimization problem that maximizes total resolvable backhaul traffic by jointly deciding BS selection, RIS phase shifts, and precoding vectors. The inherent non-convexity arising from coupling and quadratic fractional term is addressed through an alternating optimization algorithm that iteratively solves tractable convex subproblems via quadratic transformation. Comprehensive numerical evaluations demonstrate that the proposed RIS-enhanced framework significantly improves survivability from 58% to 72% under challenging high-intensity hotspot traffic conditions. Moreover, RIS provides the greatest gains for antenna-constrained systems by extending coverage to access more spare capacity of the distant BSs as well as enhancing the signal strength. Consequently, high survivability is achieved even with only two antennas per BS under moderate traffic intensity.