This is an issue I am facing as well.
Steps to reproduce:
- Publish a field group.
- Go to edit the field group.
- In the Publish metabox in the right-aligned sidebar, click the “Edit” link next to the “Status: Published” text.
- In the now-shown dropdown, choose either “Pending Review” or “Draft.”
- Click the blue “Update” button in the same metabox.
- The chosen status (whether “Pending Review” or “Draft”) is not saved. Field group remains published.