How to ensure a child theme's style.css is always refreshed when a new style sheet is deployed.

gistfile1.txt

// This gets the modified time for the current style sheet.  It caches the check for 30 seconds. 
// That's the longest you'd have to wait for a new style sheet to be forced on all visitors.
// This micro-caching helps limit drive access when the site is busy. 
// You could change it to 5 seconds on a less busy site or any value you like
function enqueue_versioned_child_style() {
        // StyleSheet date is only checked once every 30 seconds
        if ( false === ( $stylesheetmtime = get_transient( 'stylesheetmtime' ) ) ) {
                // It wasn't there, so regenerate the data and save the transient
                $stylesheetmtime =  filemtime( get_stylesheet_directory() . '/style.css');
                set_transient( 'stylesheetmtime', $stylesheetmtime, 30 );
        }

        // Version theme's CSS file in a theme
        // As long as the handle is the same, you do not need to deregister the style.
        wp_enqueue_style(
                        'roots_child', // This is the handle for the style of a child theme
                        get_stylesheet_directory_uri() . '/style.css',
                        array(),
                        $stylesheetmtime
                );
}
add_action( 'wp_enqueue_scripts', 'enqueue_versioned_child_style' );