You can mark files to be available offline in case of loss of internet. In the data panel, right click on the file and select "add to offline cache". In preferences>general, you can specify an "offline cache time period". Mine's set to 360 days, which I think is the maximum. The downside of long cache periods is the local storage that will be tied up but I don't imagine that's an issue for most of us.
You can also export (save) them as standalone Fusion 360 files for backup. From the file menu, select "export" and select .f3d to retain as much content as possible. If you save as STP or IGS you will lose most of the content and just end up with simple solid bodies.
You should be able to see your work in the autodesk360 portal, if you know what that is. Open the data panel, select your team name (your use name) and click "open on web". Hopefully your work should be there in the browser window.