Structural systems liable to asymmetric bifurcation usually become unstable at static load levels lower than the linear buckling load of the perfect structure. This is mainly due to the imperfections present in real structures. The imperfection sensitivity of structures under static loading is well studied in literature, but little is know on the sensitivity of these structures under dynamic loads. The aim of the present work is to study the behavior of an archetypal model of a harmonically forced structure, which exhibits, under increasing static load, asymmetric bifurcation. First, the integrity of the system under static load is investigated in terms of the evolution of the safe basin of attraction. Then, the stability boundaries of the harmonically excited structure are obtained, considering different loading processes. The bifurcations connected with these boundaries are identified and their influence on the evolution of safe basins is investigated. Then, a parametric analysis is conducted to investigate the influence of uncertainties in system parameters and random perturbations of the forcing on the dynamic buckling load. Finally, a safe lower bound for the buckling load, obtained by the application of the Melnikov criterion, is proposed which compare well with the scatter of buckling loads obtained numerically.