Posting this a few days late after CS couldn't resolve the issue.
The day the Qorgh ship was available as a free gift from the C-Store, I tried claiming the ship from my KDF character and kept getting the message that it was unable to complete the transaction. I tried logging completely out, using different characters (had no trouble claiming the Fed ship), but had no luck after spamming the claim key a few dozen times. I finally filed a ticket that night (ticket filed 01/29/2014 11:36 PM according to Support Center), but when they finally got to the ticket this afternoon, it was just a generic message about it being an unknown bug and to file it as a bug report (which I will do when I get in game next). Now that the giveaway has been over a few days, I noticed when I checked to see if the issue got resolved after last night's patch, that the only option for that ship for me is to purchase it, so it seems my account never got flagged as claiming the item.
I might have the name mixed up, but I was claiming the one listed as free that day and still getting that message. It was on my level 50 main character.
Comments
The Qorgh is the regular ship they giveaway free one time when you hit L20.
The ZEN store ship is the SuQob.
You also had to be L20 or higher to claim.