Sometimes a customer will abandon the credit card process after being directed to the PayPal page. In such cases the order is not considered complete and no email is sent.
If they canceled PayPal, the end user is told this on the return page when they come back to the site after cancelling PayPal, and it is suggested they contact you to complete payment.
As soon as the customer clicks the button to complete their order, the order itself will be complete so you will see it in your order area with the "paid" column left unchecked. This does give you the opportunity to reach out to the customer to see if they were still interested in ordering but wanted to give credit card information over the phone.
You should make sure that you have a message pop up when the user chooses the complete order button in Pressero. You do this on the payments tab in the site settings... Enter the warning text in the "custom message" area. You may want it to say something like "Are you sure you are ready to check out? As soon as you click ok, your order will be completed."