example.fix

var checkActiveName = jQuery('#username').val(); // just use the id

jQuery(document).on('input', '.woo_login_form', function(){ // bind to the document
    if (checkActiveName == '' ) {
        jQuery('.woo_login_form').removeClass('cdc_keep_active');
    } else {
        jQuery('.woo_login_form').addClass('cdc_keep_active');
    }
});

if (checkActiveName == '' ) {
    jQuery('.woo_login_form').removeClass('cdc_keep_active');
}