It is certainly possible to export a list of all bounced contacts along with the reason for the bounce. You can even export the bounces for an individual list (skip to List/Sphere instructions here).
Exporting Bounces from all Contacts
To export bounces from your full contact list, use the following steps on the Contacts page:
1) Click on the "Options" button in the Contacts section.
2) In the drop-down navigation, select "Show Permanently Bounced Contacts". This will return all contacts that have bounced and you are no longer able to send to.
3) Click the "Options" button again.
4) In the drop-down navigation, select "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.
Exporting Bounces from List or Sphere
*Note: This is only possible for contact lists populated by agents. You are not able to export bounces for Marketer Distribution Lists.
On the Contacts page, look to the "Distribution Lists" area on the right. If you do not see the list names, click the "Open" button in that section. Then:
1) Click on the name of the List or Sphere *of your contacts* to see the Edit Distribution List box open below.
2) Click the Options button in this area.
3) Click Show Bounced Contact to view the specific contacts in this List or Sphere that are currently in a "bounced" status.
4) Click Options again.
5) Click Export Current XXXX Contacts to download a CSV file of the bounced contacts in this specific List or Sphere.