Try with WP_Comment_Query and make sure you have the right Author ID from the Author Template.
// WP_Comment_Query arguments
$args = array (
'user_id' => $user->ID,
'post_status' => 'approve',
'number' => '10',
);
// The Comment Query
$comments = new WP_Comment_Query;
$comments = $comments->query( $args );
// The Comment Loop
if ( $comments ) {
$output.= "<ul>\n";
foreach ( $comments as $c ) {
$output.= '<li>';
$output.= '<a href="'.get_comment_link( $c->comment_ID ).'">';
$output.= get_the_title($c->comment_post_ID);
$output.= '</a>, Posted on: '. mysql2date('m/d/Y', $c->comment_date, $translate);
$output.= "</li>\n";
}
$output.= '</ul>';
echo $output;
} else {
echo 'No comments found.';
}