iFrame inside structure field not reloading

I have built a little custom field plugin that has an input and an iFrame. The input accepts a number code for a Vimeo video and the plugin generates an iframe using that code. It works well, but when I put the field inside a structure and use the arrows to navigate through the structure, the iframe does not reload to show the correct video. Is this a problem with my plugin or an issue with iframes in structure fields in general?

I’ve realised I can replicate exactly what I want with the new Blocks field :sweat_smile: But for future reference, how do you get iFrames to work in structure fields?