Thank you for the proper details, I think I see what the problem is there.
In this case the lucky thing is that the pop-up script does not duplicate the elements, so after the first click everything stays as it is. This makes this issue resolvable, with a small custom code.
Add this custom code to the functions.php in your theme/child theme directory (copy from line 3 only!). Before editing, please make sure to have a full site back-up just in case!
This will add a small script to the page, which will re-initialize the search when the pop-up magnifier is clicked for the first time. Let me know if you need help with it!Best,
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