Fisheye cameras are effective tools for autonomous robotics applications in unstructured, non-built environments due to their wide field of view. The wide view is particularly beneficial for simultaneous localization and mapping (SLAM) and sensor fusion. In forest environments, the horizon is generally unavailable and therefore conventional horizon stabilization is not possible. In particular, frame instability commonly affects small ground-based autonomous vehicles with multiple tracking tasks due to significant rotations, especially when navigating rough forest terrain. To address these challenges, we propose a robust method for stabilizing the fisheye video stream by minimizing the image difference of sequential frames through the use of rotational pixel maps. A precomputed library of pixel maps is generated for real-time computation. The stabilized output can improve the reliability of SLAM and sensor fusion applications. We also review current video stabilization techniques relevant to small autonomous vehicles and highlight the unique challenges faced by forested environments. Our experimental results are demonstrated through two use cases in different environments with performance metrics including memory usage, processing speed, location error, and angular deviation per path length. Our proposed method achieves real-time frame stabilization at a practical frame rate of 30-40 frames per second (fps) in low-resource computing environments with  horizontal and  orientation errors.