The paper analyzes the influence of static preloading of the reinforced concrete frame of a building on its relative robustness index under the scenario of a column removal. The study was based on quasi-static finite element analysis, taking into account physical and geometric nonlinearity. The constitutive diagrams of concrete took into account the rheological properties of the material in the static-dynamic loading regime. For this purpose, the integral module concept proposed by Bondarenko was adopted. Numerical modeling has shown that the values of fracture load and the relative robustness index decrease for model accounted for rheological properties of concrete compared to model that did not consider such properties. The revealed effect is caused by the growth of deformations in eccentrically compressed members as a result of creep and shrinkage. Thus, the factor of long-term operation can have a negative impact on the robustness of reinforced concrete structures under accidental actions, such as a column removal scenario. This effect should be considered in the structural design of reinforced concrete building frames.