Dynamic soaring is a technique by which wind gradients are utilized to extend flight times. This was originally observed amongst birds like albatrosses, eagles and is exploited in the flight of UAVs. Earlier works have focussed on generating dynamic soaring trajectories including periodic orbits through various methods like Gauss-Pseudo spectral method, IPOPT, numerical integration methods etc. Such orbits find applications for surveillance UAVs. However, there has been no study reported on the stability of the periodic orbits and its dependence on any parameter of the system. Stability of dynamic soaring orbits is important since the trajectories can get disturbed by a strong gust or crosswinds causing the UAV to veer off-course. Although control system can be designed, a stable orbit can reduce the control effort and power. In this paper, the problem of studying stability is treated from the context of a periodic coefficient system. For assessing the dependence of stability on system parameters like wind shear, drag coefficients and surface-area-to-mass-ratio a Monte-Carlo based approach is used. A distribution of Eigenvalues is obtained to study this dependence. © 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.