Just click the Continue button and the download will do just that.
I experienced the same - that the download stopped by itself, and completed the task by the described procedure above.
You may find that some effects and extras have been relocated. I needed to guide the program upon opening a project.
I suggest you install PhotoStory Deluxe and download all extra content prior to opening any projects. There is also a patch you should install after completing install and download and before opening projects.