Yup, the RV Storage would pull something like that. Is it some looping seamless video used as a background? It happened to me a couple of times with them, too. Smaller videos could be converted to Animated GIFs and played as images. For larger videos used on more then one device you might want to use another Internet hosting service, which sux if you are already paying for the RV Storage, or upload separate files for different players - this way you will cut the number of requests sent for the same file.
If you are using Rise Player, images and videos shown by the respective Widgets will be stored in a persistent cache. Which means the continuous downloading will not occur, and you don't lose the files on reboot.
I just wanted to let you know that our new Cache has been deployed, and will be rolling out to all Displays in the next week. Once your Display is updated, we are confident that this issue will be corrected.