This paper deals with the numerical bifurcation analysis of the contact loss between a pantograph and an overhead rigid conductor line in a railway current collection system. In the previous study, we modeled this problem as impact oscillations of an intermediate spring-supported beam excited by an oscillating plate. We have already derived the modal interaction relationship equations that describe the velocities immediately after an impact as functions of the velocities before impact for each vibration mode. A numerical calculation using these relationship equations was performed to clarify the impact oscillations with multiple vibration modes. In this paper, we propose a numerical technique based on maps that transform the state of the system at the impact to the subsequent state at the next impact. This numerical method produces stability analyses of the fixed points of the map that describes an impact oscillation with multiple modes. These results can differ surprisingly from the expectations based on a single-mode solution. These results are compared with experiments undertaken in our laboratory, utilizing a thin stainless steel beam. The typical features of impact oscillations, which were theoretically predicted, were confirmed qualitatively.