Since upgrading to ArcGIS Pro and therefore the 2.01 version of the API I have noticed that when clone_items is run on a webmap with the "copy_data" set to True and "search_existing_items" set to False then the newly created webmap only respects those rules (i.e. points at cloned copies of the Hosted Feature Layers) for the first item it encounters.
If your webmap contains two different hosted feature layers, it clones them both, and the first instance in the webmap is correctly referenced, but the second one points back at the original hosted feature layer.
This is incredibly frustrating behavior (a halfway house of what it should be doing) and is surely a bug?? Any advice on whether ESRI are aware/fixing it or suggestions for a workaround are gratefully received!!