Order posts by month – in custom taxonomy template

Save the current month in a variable and check it for each post, only output it when it changes:

$current_month="";

while( have_posts() ):
    the_post();

    $this_month = get_the_time( 'F' );

    if( $this_month != $current_month ){
        $current_month = $this_month;
        echo $current_month;
    }

    the_title();

endwhile;