While creating the very first post for this blog, I ran into an issue with uploading my custom-created GIF. The GIF was working everywhere else except in my post.
It turns out I had selected 'medium' as the image size when inserting it into the post. When you choose to select a different size, I'm guessing WP reformats the image, which is why the GIF was not working.
Make sure you select Full Size in the Attachment Display Settings when inserting media.