Action video is often lacking clear persistent references to stabilize video with – they either are not present in the frame for very long, or often compressed out of frame as the codec is trying to spend most of its bandwidth on moving objects in the shot.
Deshaker, a plugin for Windows program VirtualDub, with its capability to find and track multiple visual references (literally hundreds of them) automatically from frame to frame is the king of action video stabilization. (It works on Linux, too, see below).