This happens to me often.  Adverts and social networking links are frequent
culprits.

So the question is: are the GIFs actually stored on the site you're mirroring? 
If they are being fetched from another host, you'll need to add that host to
your list.

While viewing the original site in your browser, right-click on the errant GIF
file and inspect its properties to see if it's located on the same host.