It seems like that cron is not sending out the overdue e-mail automatically to customer when billing date is reached.
Did you followed the wiki page for recurring invoices?
If no, please take a look and follow the instructions.
If yes, how did you set up the cron? If you used the standard Linux cron you should get either get a cron error or an PHP error of the script. In both cases we need to know which error is thrown.