This article investigates the problem of enhancing the robustness of multi-story reinforced concrete building frames under progressive collapse initiated by the local failure of load-bearing elements. Modern approaches to analyzing structural resistance, including experimental and numerical methods, are reviewed. Particular attention is paid to the influence of reinforcement type, loading conditions, and the flexibility of nodal connections on the system’s behavior under emergency conditions. Numerical calculations of the dynamic force redistribution in a reinforced concrete frame following the sudden removal of a column were conducted. The simulation was performed considering material nonlinearities and geometric nonlinearity. Various levels of service load, ranging from 30 to 90%, and two reinforcement schemes, characterized by different failure modes (ductile and brittle), were investigated. The results showed that joint flexibility significantly affects the structure’s ultimate limit state, particularly in sections where failure occurs due to concrete crushing (the influence varies from 45 to 65%). The stiffness of the nodal connections, to a lesser extent, alters the absolute values of the internal forces but dictates the dynamics of their redistribution. Under high loads (0.9 qs), an avalanche-like (catastrophic) collapse is observed in the case of brittle failure, whereas with ductile reinforcement, the system maintains stability. The importance of accounting for joint flexibility when designing buildings with enhanced resistance to progressive collapse has been established. The obtained data can be used to optimize structural designs and develop methods for strengthening reinforced concrete frames.