I made a Loom which might make things clearer. This is the first time I've had this issue with Prismic and in the past, I've uploaded multiple articles where the gifs function and post as they should.
But as I said in the title, gifs that I've uploaded and then added to an article disappear once I save the article.
I've had a look at the recording, thank you for sending this. What I could see is that you is experiencing a known error where images cannot be added to lists in the rich text field.
We have discussed this at greater length in the following thread:
The solution for now is to make sure the image isn't added inside the list, but to make sure it's added between list items instead. Even better would be to use slices and model it as so: