Custom Post Type "Pending Review" Broken

One of my custom post types is behaving strangely when it comes to posts “pending review.” If I publish a post and then later change its status to “pending review,” it behaves as expected. If I create a new post and immediately assign its status as “pending review,” the “Pending” count increments, but the post does not show up in the list of pending posts. It does, however, exist in the database.

I created a new custom post type to determine whether this is an issue with WordPress at large or just with the post type in question. The new post type worked just fine, so this must be a problem with just the one specific post type.