In the context of growing need of decarbonization in industry in general and aviation in particular, hybrid propulsion has emerged as a promising trend in recent years [1,2]. Among a number of other requirements, this technology requires incorporating a reliable and efficient power transmission system, in which the overrunning clutch represents one of the key components. With this motivation in mind, recent efforts by the authors have been dedicated to the development of detailed mathematical models for the accurate simulation of clutch behaviour under different operating conditions. Building upon [3], the current model can capture the complex interactions induced by contact between sprags and the outer and the inner races within the clutch, as well as kinematic nonlinearity, including potential disengagement. In addition, the model enables the prediction of the dynamic behavior of the sprag and, consequently, rollover failure. This is a catastrophic failure that occurs due to the high-amplitude vibrations of the sprag. Powertrain rapid acceleration/deceleration events, acting as system impact loads, can lead to nonlinear oscillations of the sprags, with amplitudes that depend on a combination of parameters and external forcing conditions. As this phenomenon represents a potential hazard for the whole aircraft, a thorough investigation is in order. In this contribution, we perform a parametric analysis to shed light on the mechanisms behind the unstable clutch dynamics. We show, in particular, that the onset of stability depends on the first elastic torsional modes of the system. Hence, the formalism of nonlinear normal modes is exploited to derive safe operating zones in the parameter space. This is achieved through a computational implementation of pseudo arc-length continuation based on the harmonic balance, coupled with specialized routines for the stability evaluation of cycles along branches of nonlinear modal solutions. [1] B, Etienne Demers, et al. "Modeling and simulation of novel electric/hybrid electric multicopter architectures for urban air mobility." 2021 AIAA/IEEE Electric Aircraft Technologies Symposium (EATS). IEEE, 2021. [2] Stevens, Mark A., , et al. "RVLT Concept Vehicle Powertrain Arrangement Study and Candidate Powertrain System Test Arrangements". No. E-20057. 2022. [3] P. Pescetto et al., "Electromagnetic and Mechanical Modeling of Medium Voltage PMSM for Hybrid Regional Aircraft in Faulty Conditions," 2025 IEEE Energy Conv