Why is there no Pinterest button on some posts?

Pinterest pins an image. On a post with no share picture and no featured image there is nothing to pin, so the button hides itself rather than opening a dialog that produces a blank pin. Set a Default share picture under Networks → Open Graph Tags and every post has something to pin. That picture is only used while Add Open Graph and X card tags is on and no SEO plugin is active, because then the tags are the SEO plugin's. An SVG is not pinned.

While those tags are this plugin's, a post behind a password has no Pinterest button either, even with a share picture or a featured image. The buttons sit under the password form, where anybody can read them, and a Pinterest link would carry the picture's address to people who have not entered the password. Such a post is shared with its title and address only, as its Share buttons box says. For a visitor who has entered the password, the buttons are as they are on any other post. With the tags off, or while an SEO plugin, your theme or Jetpack writes them, the Pinterest button on such a post pins its featured image, as it always has.