Unity Movie Texture - Skipping First or Last Few Frames

I have added a movie texture to my game (file type is .mp4) and I have been able to get it to play and loop. However, in Unity it is not a perfect loop, and stutters when it restarts. The video I am using is a perfect loop, so it seems like it is skipping either the first few frames or the last few frames of the video when it is being played in Unity. Does anyone know why this would happen when I play the video looped in Unity? Also, some additional notes, I have the video set at a constant 30 FPS and there is no audio track tied to the video.