It is certainly possible to export a list of all bounced contacts along with the reason for the bounce. To do so, use the following steps:
1) Go to your Contact page.
2) Click on the Options button in the Contact section.
3) In the drop-down navigation, select "Show Permanently Bounced Contacts". This will return all contact that have bounced and you are no longer able to send to.
4) To export the list, click again on the Options button, this time selecting "Export Current XXX Contacts". This will download a CSV file to your desktop.
5) Open the CSV file you just downloaded. It should be named export_contacts.csv.
6) The 4th column is "Bounce Reason" which displays the reason given by the recipient's server at the time of the bounce.