I don't have a solution yet but I encounter this every month when I send bills. It sends 9 or 10 emails and then it pops up with the message - Quickbooks is unable to send emails due to network connection failure. It probably will let you send more the next day but I send all my bills the same day so I click on save the attachment after clicking to send it - then manually mail it. What a colossal PITA.
