Something is probably wrong within the app, try to uninstall it, restart the device and install the app again. Make sure you have available storage for the app to work properly.
In some Android devices there is a function called "Don’t keep activities". This should not be checked for the Storytel app to work. You can find it under Setting -> Developers options.
If you have an Android device: a lot of books in your book shelf can affect the apps performance. If your app is slow, crashing or not responding try to remove books until you have under 200 in the bookshelf.