When I create the blog post, it looks like an image is showing up, but when I publish it, the image doesn't show up. There are other GIFs in the same post that do show up. This is the post https://www.wibidata.com/blog/wibi-interns-2014-our-summer-in-gifs
If the images that do not show up are coming from tumblr, then it's because you are linking to them with http protocol (see your DevTools). Your site seems to enforce SSL, but links to images on tumblr are coming from non-SSL (http protocol).
Try using them with secure protocol (
https) or without (instead of