GeoDirectory hides the sort dropdown on search results on purpose. Results are already ordered by what the visitor searched for, so the sorting options you set up only appear on category and post type archive pages.

How search results are ordered

• When the visitor searches near a location, results are sorted by distance, nearest first.
• When they enter keywords without a location, the best matches come first. A match in the listing title counts for more than a match in the description.
• When neither applies, the default sort you set for the post type is used.

Where your sorting options do apply

The options you add at Places > Settings > Sorting show in the sort dropdown of the GD > Loop Actions block on archive pages, and the one marked as default orders those pages. Changing or Adding New Sorting Options explains how to set them up.

A search results URL still accepts a sort_by parameter, for example &sort_by=post_title_asc, if you link to a search with a fixed order.