Able to define video header only once

I’m able to set the header video only once. After that, going back to “Customize” > “Header Media” from home page I get “This theme doesn’t support video headers on this page.” Same whether whether using a blog or a static page as front.

Changing to another theme and then back to Twenty Seventeen seems to reset the situation and I can change the video header, but again, only once. Wouldn’t mind this for a single blog, but as a blog network admin there’s bound to be a lot of questions about this behaviour.

I’m running WordPress 4.7.1 multisite installation with subfolder structure. Twenty Seventeen is version 1.1.