While Atticus does have some offline functionality, you’ll have to make sure you’re logged into Atticus and have the program open in your browser (or the app) before you lose your internet connection.
While offline, you can write and edit your text, and your changes will be synced to the server once your are back online. While working offline, I strongly recommend you also hit the Save button in the top right, next to the ? button, at the end of each session and keep the JSON file that is generated, just to ensure that all of your content is backed up in a second location.