stop shortcode stripping in category and archive pages

Shortcodes are stripped from the excerpt before filters are applied. Try something more like this:

function tsc_execute_shortcodes_in_excerpts( $text, $raw_text ){
  if(empty($raw_text)){
    $text = get_the_content('');
    $text = apply_filters('the_content', $text);
    $text = str_replace(']]>', ']]>', $text);
    $text = strip_tags($text);
    $excerpt_length = apply_filters('excerpt_length', 55);
    $excerpt_more = apply_filters('excerpt_more', ' ' . '[...]');
    $words = preg_split("/[\n\r\t ]+/", $text, $excerpt_length + 1, PREG_SPLIT_NO_EMPTY);
    if ( count($words) > $excerpt_length ) {
      array_pop($words);
      $text = implode(' ', $words);
      $text = $text . $excerpt_more;
    } else {
      $text = implode(' ', $words);
    }
  }
  return $text;
}

add_filter( 'wp_trim_excerpt', 'tsc_execute_shortcodes_in_excerpts', 10, 2 );

That basically re-runs wp_trim_excerpt() on the content (minus shortcode stripping) if it was trimmed to begin with. If you want to target your shortcode only, you could do something like this after get_the_content(''):

$text = str_replace( '[tsc', '{tsc', $text );
$text = strip_shortcodes( $text );
$text = str_replace( '{tsc', '[tsc', $text );

Hope that helps.