The Search and Web Content Search portlets currently do not have mobile responsive components.
This was reported as a bug in LPS-41152, but is being addressed in this feature request as the fix is more involved.
"We shouldn't be changing portlets UI for desktop. And the search portlet is a special case because lots of themes instantiate it using portlet_runtime and this approach is likely to break some of them. I think in this case we can't make use of the navbar responsivity. We'll have the style it ourselves." -Bruno Basto
The fix must be specific and take Bruno's remarks and mobile design into account.