The field is not gathered on the SELECT for that ...
You could try to customize the SELECT statement so the field is available to you in the listing ...
Or, you can use a handy dandy look up function that is useful for any field in the products or products_description tables:
zen_products_lookup($product_id, $what_field = 'products_name', $language = '')
Example: zen_products_lookup('3', 'products_date_added');
Where 3 is the products_id ... so just use it with the products_id for the listing where you want to call it ...
Otherwise, you would need to actually do the changes for the code that gathers the information for the products listing as well as the search ...