Assuming that your latest save game was made from that console, when cloud storage goes down, just go to Settings -> System -> Storage and move your saved games from cloud storage to hard drive. Once cloud storage is back up, just move it back into cloud storage.
As others have said, there's 512mb cache on each console (shared between all profiles on that console, and it's separate from the 512mb of personal cloud storage). That stores your latest saves, which is why when cloud storage is down, you just have to move it from the cache.