Your iOS devices get backed up whenever you sync with iTunes, and you can also choose to backup your data to iCloud in the Settings app. These backups include your Studies data, so restoring a backup should bring back your old data should anything go wrong.

One downside of restoring a backup for your whole device is that it restores all data, not just your Studies data. There is an option in Studies that allows you to export your whole Library, for backup purposes, or transfer to another device.

To do this on iPhone, go to the main menu by tapping the button top-left in the Library, and select Send and Receive. Tap on Export Library…, and then choose a file handling app to export to.

On iPad, you tap the Sharing button 3rd from the right in the toolbar at the top, and select Export Library….

A good choice for a file handling app is Dropbox. You can sign up free at dropbox.com, and they have a free app available in the App Store.

You can import an exported Library file by loading it in a file handling app like Dropbox, tapping the file, tapping the action button (box with arrow), and choosing Open In.... Then choose the Studies app.

If you do decide to import an exported library file, be aware that it will completely replace any data you currently have in the app.