If you need to duplicate a project in you account, you need to first Export the project, and then Import it again.
Export a Project
Click on the blue menu button in the top-right of the left-hand sidebar in ParseHub, with a project open.
Click on the "Export" button.
Save the project on your computer, on the Desktop.
Import a Project
From the list of projects in the ParseHub menu, press the blue "Import Project" button.
Choose the project that you saved on the Desktop to import it.
After the project loads, save the project via the blue menu in the top-right.