Hi!
Thank you for the details. I think I see the problem, it appears to be a malformed CSS rule related to the theme:
[code]media only screen and (min-width: 1024px) {
.fusion-mobile-menu-search {
display: none!important;
}
}[/code]
I cannot exactly tell which file this is originated from, as it is minified. It basically forces to hide the mobile menu, so it is invisible any time on screen widths above 1024 pixels.
Once that rule is removed, it will fix the issue immediately. Unfortunately there is no alternative solution in this case, as any other higher specificity CSS rule would override this, and make the search container visible at all times.
You might have to ask the theme author how to remove this, if this is not a custom CSS rule you have added to the theme.