The tool you are using to display favorites is using an API that is not available anymore.
You should replace the iframe with an [node:10248, title=“embedded timeline”].
To have all the details read [node:10248, title=“that page”], but in short:
- go to twitter.com
- sign-in if you are not
- click on the gear on the top right corner
- click on "Settings"
- click on "Widgets" (it's on the left)
- click on "Create new"
- for the timeline source choose "Favorites"
- fill the other fields
- click on "Create widget"
Paste the generated HTML code that's on the bottom right on your website.