Do you see the field, column added to the DB records (Media_File table)? Is it also in the CMS_Class table, for the media.file class name and check the ClassXmlSchema and ClassFormDefinition XML definitions - the custom field should be there too.
Then, how are you exporting this? The single module export probably does not cover this - you may need to export the entire site and actual media file objects (media files). Or, use content staging to transfer these changes.