I use a different theme named Team Talk (Premium). Since I use this theme, I don't receive the new comment notification by email. I don't know where to look at but I found this in my new theme :
function get_content_html_for_comment($comment){
$comment_html = "";
// Get the comment data
//switch on the output buffer
ob_start();
// Allow the email to the author to be sent
wp_notify_postauthor($comment_ID, $comment->comment_type);
$max_depth = get_option('thread_comments_depth');
$args = array ('max_depth' => $max_depth);
//render the content to the output buffer
//call _ht_comment
echo _ht_comment($comment, $args, $this->calculate_comment_depth($comment));
//the content will now be in the buffer, so get that
$comment_html = ob_get_contents();
//restore buffer
ob_end_clean();
return $comment_html;
So, it seems to allow to receive notification but it doesn't work.