All images show in Media Library, only some show on Insert Media

Some time in the last several weeks, I started having some media items not show up when trying to add media to a page or post. These were all media that had been in my libary already. If I go to the Media Library, I see all of my media. If I go to insert media into a page, some media are not there. I only see about 1/3 of my total media library.

I have tried enabling/disabling plugins that had recent updates, I have reinstalled WordPress 4.5.3, and I have changed my theme. I haven’t tried disabling all of my plugins, and I haven’t tried restoring an old backup, but I’m going to try that. Any other ideas why suddenly media won’t show on the Insert Media popup?