Hi,
Looks like the theme sticky header script is making a duplicate of the search – one for the regular header, and one for the sticky one. That is an extremely bad programming practice – as event handlers are not copied over, and cannot be copied in any way either.
There is a special bypass option in the plugin that you can try to activate, here: https://i.imgur.com/AAeXYHa.png
However that may still not work, this should be resolved from the menu script unfortunately.