Index: wp-includes/cron.php
===================================================================
--- wp-includes/cron.php	(revision 20794)
+++ wp-includes/cron.php	(working copy)
@@ -256,6 +256,7 @@
  * @return null When doesn't need to run Cron.
  */
 function wp_cron() {
+	global $current_blog;
 
 	// Prevent infinite loops caused by lack of wp-cron.php
 	if ( strpos($_SERVER['REQUEST_URI'], '/wp-cron.php') !== false || ( defined('DISABLE_WP_CRON') && DISABLE_WP_CRON ) )
@@ -264,6 +265,10 @@
 	if ( false === $crons = _get_cron_array() )
 		return;
 
+	// Don't process cron for suspended blogs. 
+	if ( is_multisite() && ( $current_blog->archived || $current_blog->spam || $current_blog->deleted ) )
+		return;
+
 	$local_time = microtime( true );
 	$keys = array_keys( $crons );
 	if ( isset($keys[0]) && $keys[0] > $local_time )