Is it possible to limit the number of frontend submissions to one per user?

There is no built-in functionality at this point, but it should be possible using a custom filter function on the user_has_cap hook. The following code (add to your theme’s functions.php file) will count the number of published posts of a certain type by a specific user and remove the permission to add new posts for the specific post type if the user has already published a post.

Note: You need to change the ‘directory_dir_ltg’ part to the post type of your directory listing. The post type name is viewable from:

Directories –> [Your Directory] –> Content Types.

add_filter('user_has_cap', function($allcaps, $cap, $args) {
// Some initializations
$post_type = 'directory_dir_ltg';
$cap_to_check = 'drts_entity_create_' . $post_type;
$limit = 1;
// Bail out if this is not the capability we are looking for
if ($cap[0] !== $cap_to_check) {
    return $allcaps;
}
// Bail out if the current user doesn't have the capability currently
if (!isset($allcaps[$cap_to_check])) {
    return $allcaps;
}
// Bail out if the number of posts by the current user is below the limit
if (count_user_posts($args[1], $post_type) < $limit) {
    return $allcaps;
}
// Remove the capability
unset($allcaps[$cap_to_check]);
return $allcaps;
}, 10, 3);