There are various things this could be, but if the other emails are working it sounds like a config issue, so check this.
In admin, take a look in
System > Configuration (TOP MENU)
Then;
Sales Emails (LEFT MENU),
Check which contact is sending the email - eg Sales Rep. While you're here, add your personal email to the 'Send Order Copy To' field for testing - make sure it's not the same domain as the website, so like a gmail.com address or similar. Also check what email template is set and make sure it exists. If 'default from locale', check;
app/locale/[DEFAULT COUNTRY CODE]/template/email/sales/order_new_guest.html
app/locale/[DEFAULT COUNTRY CODE]/template/email/sales/order_new.html
Now go and check the email address set for the sender (New Order Confirmation Email Sender) - eg Sales Rep, these are in;
Store Email Address (LEFT MENU)
Ensure there is a value for email address and name, and it is correct. If it is, go and place an order using another personal email address at a different domain like gmail etc (not the same email address you set for the copy).
Hopefully the emails you do or dont recieve now will help you corectly trace the issue.
EXTRA
If you still receive no emails, couple of things to look at;
Check System > Config > Advanced and make sure smtp isnt disabled (seems unlikely as your other emails are sending)
Make sure paypal pro is setting the status to processed
Try changing the email address being used to send them, eg Sales
rep. Try changing this to an email address with a different domain,
such as gmail.com etc. If this works, then you need to look at how
your domain and email has been setup on the server.
Check your error logs /var/logs/