I have found the following problem.
When a I first publish and broadcast a post, the image attachments are not properly copied to the other blog which breaks the featured image.
To be a bit more specific, the 'posts' of type 'attachment' ARE created in the wp_posts table, but in the wp_postmeta table, the fields _wp_attached_file and _wp_attachment_metadata are blank. Also, the actual file is not copied into the 'uploads' folder on the server. The 'thumbnail' field IS copied and refers to the 'attachment' post correctly, but since that entry doesn't contain any data, the featured image does not show.
However, after publication of a post, if I click 'Update' on the post, all of this is fixed - the files are immediately copied over to the server and the database fields are correctly filled in and so the featured image displays correctly.
Its not a massive deal, but I do have to remember to 'Update' after publication - anyone with any idea how to fix this?