A couple of things.
If you (or your author) adds an image to a post on your blog, they need to add that image to your blog's media library, and then add that media library image to the post. If the image is hotlinked to another blog, on WordPress.com or elsewhere, you do not control that image, the other source does, and if they delete it on their site, it disappears from yours.
As it turns out, every image I am seeing in posts on your blog on page 2 are being linked to other blogs. Even if the image was uploaded to your media library, those authors are not using those images but are linking back to their own.
If there are posts where this is not the case, please post the link to the specific post so I can take a look at it.
In general, if images are disappearing, please encourage your authors to only add images to your blog if they add them via the Add Media button from images they uploaded to your media library.