This problem most often occurs when you have manually copied media using FTP or the Plesk File Manager into WordPress's wp-content/uploads folder.
When you upload media using the standard WordPress media upload function it does two things:
1. Creates an entry in the WordPress database that holds additional data about the media file, and
2. Uploads the actual media file to the wp-content folder
Those two things work together to make the media library work. If your import fails to import the media files, then the database entries don't get created, so even if you copy the media over, they won't appear in the media library.
That said, the media files *will* still show on pages and posts. They just won't be selectable to insert into pages and posts from that point forward.
The Add From Server plugin will allow you to re-import that media from the wp-content/uploads folder into the Media Library.