If you suspect that there is an issue with emails related to orders, test the ASPDNSF email setup from Configuration >> Email >> Test All. (see http://screencast.com/t/oJiok1HvSL) If everything is functioning properly, you will see a "Successful" notifications for Receipt, New Order & Shipped emails. If any of the 3 reports are "unsuccessful" notify INSite via the "Submit a Request" button from the main navigation, or via email to firstname.lastname@example.org.
Receiving email is a multi-layered issue, with no "perfect" solution. At the user, employer, (for those using work addresses) and ISP level, there may be spam filters in place that prevent email from arriving in the recipient's Inbox. Be sure to ask anyone reporting an email issue to #1 - check their spam/junk folder for the email, and #2 add your "Receipt Email sends from (E-Mail address)" as a safe (white-listed) sender, as that is the origination email address for your receipts.
You may check when the email was sent (and/or re-send a receipt) within the "General" section of the order. (see http://screencast.com/t/0wtJ0IoCeyhX) If a customer requests that you fax or mail a copy, select "Receipt" then "Print Receipt" within the order. (see http://screencast.com/t/c1e9abWc)