I have an existing product that I need to add to a second category. Its below the root, its enabled but it never shows the item.
Its a configurable item but that should not make a difference.
Moving products from one category to another is not to be issue in Magento. Please reindex and clear your cache and check... Cheers
Also one hint, check website/store view the category belongs to. Maybe it is not the same as the one you check at the front-end.