Would the project you're trying to get a local copy of happen to be a team project file or a regular RP file? You can check what type of file your shared project is by logging into and clicking into the workspace containing the project. A regular RP project will appear with a blue file icon while a team project will appear with a pink file icon:
If the project you're trying to access isn't a team project, you (or the original user who uploaded the project) can convert it to one by opening the project's RP file in Axure RP and then going to "Team > Create Team Project from Current File" in the menu. Then in the "Create Team Project" dialog that appears, you'll be able to select the same shared workspace to host the team project in. The users that have been invited to that shared workspace should then be able to see and get local copies of that team project through the "Get and Open Team Project" menu option.
I hope this is helpful! Please let me know if you have any questions about this or if your project already happens to be a team project.