High-speed rotating machinery supported by active magnetic bearings (AMBs) is readily available in industry, where AMBs are typically used in machinery that remains fixed on stationary platforms during operation. However, in the transportation industry, this kind of machinery faces additional challenges due to external disturbances caused by the moving base. The limitations of the AMB systems to levitate the rotor in such operating conditions require thorough investigation. This work aims to contribute to this by analyzing the stability of a nonlinear, electromechanical model of a rigid rotor installed on a moving platform and supported by AMBs with proportional-integral-derivative (PID) control that were originally designed for stationary application. The nonlinear dynamic behavior of an existing rotor-AMB system is analyzed, to determine its performance limits in these more challenging operating conditions. The simulation covers different unbalance settings, various external perturbations, and rotor positions on the moving base. The results demonstrate that the additional gyroscopic forces generated due to the different amplitudes and frequencies of base motion pushes the AMB currents to their limiting value, causing instability in the system. In contrast to previous studies, this fully nonlinear approach in modeling and simulation provides a correct picture of the AMB system's admissible operating range in the presented scenarios.