Is it possible to make a video texture repeat in the compositor? I have an animated overlay I want to use, and I have composited my project how I want, but I can't figure out how to make my animated overlays repeat. I want to know if there is a way to do this outside of the VSE if at all possible. 

I am using the Video Clip node, but the video clip is only 57 frames long, and I need it to repeat for the full 400 frames of the animation. Can this be done outside of  the Video Sequence Editor in the video editing stages?
Load your video not using the Movie Clip Node but with the Image Sequence node (yes you can load video files in the image sequence clip).

Then enable the cyclic option and your video file will repeat on a loop.