Login to prostores store admin and go to Store -> Store Log... click on the End of log link and then search for the invoice # of the failed order email... Most likely there is a format error of the email within the customer record, or the mail service has failed on the mail server defined in store admin -> store -> mail.
There's another possibility if you're using StoreSense version 5.6.1. If the customer's last name contains a comma, the order notice will not be emailed to them... it's fixed in 5.7+