This paper investigates the application of reconfigurable intelligent surfaces (RISs) to improve fronthaul link survivability in cell-free massive MIMO (CF mMIMO) systems. To enhance the fronthaul survivability, two complementary mechanisms are considered. Firstly, RIS is set to provide reliable line-of-sight (LOS) connectivity and enhance the mmWave backup link. Secondly, a resource-sharing scheme that leverages redundant cable capacity through neighboring master access points (APs) to guarantee availability is considered. We formulate the redundant capacity minimization problem as a RIS-assisted multi-user MIMO rate control optimization problem, developing a novel solution that combines a modified weighted minimum mean square error (WMMSE) algorithm for precoding design with Riemannian gradient descent for RIS phase shift optimization. Our numerical evaluations show that RIS reduces the required redundant capacity by 65.6% compared to the no RIS case to reach a 99% survivability. The results show that the most substantial gains of RIS occur during complete outages of the direct disconnected master AP-CPU channel. These results demonstrate RIS's potential to significantly enhance fronthaul reliability while minimizing infrastructure costs in next-generation wireless networks.