I do not understand, when I went to the page you referenced and searched Houston, Texas, using drop down menu as 100 miles , I saw the dealers and the map.
I noted you were using a child theme. I noted you had disable initial directory on and hide map until search. Is your radius under results settings set high enough? I do not have any other suggestions.
I cannot troubleshoot or recreate your issue. If you need the developer to assist you there is a paid support option.