Automatically minify css if it's been updated.

automatically-minify-css.php

<?php

/**
 * Automatically minifies style.css and writes output to style.min.css
 *
 * @author Justin Tallant
 * @param boolean $minification_is_on when true ends execution of the function
 * @return void
 * @link http://justintallant.com/switching-between-minified-and-non-minified-css-and-js-files-in-wordpress/
 */
function jt_minify_css($minification_is_on = true) {

    // if minification is on we shouldn't be editing the non-minified stylesheet
    // so there is no reason to check if it has been updated
    if ( true == $minification_is_on ) {
        return;
    }

    $last_modified = filemtime( get_stylesheet_directory() . '/style.css' );

    add_option( '_stylesheet_last_modified_', $last_modified );

    if ( get_option('_stylesheet_last_modified_') != $last_modified ) {
        update_option('_stylesheet_last_modified_', $last_modified);
        $command = 'cleancss -o ' . get_stylesheet_directory() . '/style.min.css ' . get_stylesheet_directory() . '/style.css';
        exec($command);
    }
}
jt_minify_css($jt_use_minified_files);

This won't work unless you have Node installed on your server and have installed the clean-css package.
See this blog post for details http://justintallant.com/switching-between-minified-and-non-minified-css-and-js-files-in-wordpress/