Some games only limit you to having one save file at a time. Can you set up an offline profile (i.e. make a new account on your xbox which doesn't even have XBL silver) and play your game on that account?
Or would that be considered "game sharing." It's a downloadable title I got off of XBL games on demand if that matters. --- http://www.gamefaqs.com/boards/615804-the-elder-scrolls-v-skyrim/64275451 - Skyrim Level 81 Guide