Hi!
It took me a while, but I think I have found out what happens there. The search uses a form to store some of the data, and if there are no filters selected, they are not displayed (but still there). Apparently, either the form plugin script, or something else seems to be manipulating the form data – it sets all the checkboxes there to ‘unchecked’, even though they are checked by default.
Unfortunately, I don’t think I can do anything to prevent that, the checkboxes seem to be automatically changed via a 3rd party script. I cannot check which one though, it does seem to be executed on page load. If removing the nex forms does the trick, then I guess one of their scripts accidentally unchecks them.
Since I see it is a test page, I have added a VC section with a form + a checked checkbox there for testing. You can see it on the front-end that it gets automatically unchecked once the page loads: https://i.imgur.com/w3uKYNC.png
You might have to contact the form author to look at this issue, feel free to share this information with them, they might be able to tell which line is at fault there. First make sure, that de-activating the form plugin does resolve the problem. If so, then it is very likely related to it.
I also made sure it is not related to the search plugin, I de-activated it temporary so that no scripts are loaded from it, and the issue was still present.
I hope this helps!