Your StoryMap saves automatically as changes are made to it. However, technology is not always perfect and you may exit StoryMaps without your changes being saved. Make sure you keep an eye on the saved icon on the left of the upper navigation bar.
To circumvent any automatic saving issues, however, you can choose to publish your story. This will publish your StoryMap, as is, to the web, ensuring that the work you put in will not be lost. To publish your StoryMap, there is a publish dropdown on the right side of the upper navigation bar. When selecting the dropdown you will be given the option to publish your StoryMap publicly or privately. You may choose to publish your StoryMap privately but keep in mind that only you will have access to your story. To share your StoryMap with others, you must choose the public option.
Once published, whether publicly or privately, you are still able to edit your StoryMap. To edit it, select the "Edit story" option in your top navigation bar. You will notice, after publishing your StoryMap for the first time (and then returning to edit it), the orange box in the top navigation bar that says "draft" will now be teal and read as "published."