Embedding Instagram in WP

We regularly embed Instagram content on our site by just pasting the URL of the Instagram post. We’ve found that while this works normally for the first few hours after a post goes live, eventually all the Instagram embeds go dead and the page just displays text links and no images.

Any idea what is happening here and how this can be fixed?

Sample page: https://www.rap-up.com/2018/06/10/kanye-west-41st-birthday-party/

The page I need help with: [log in to see the link]