kernel: disk3s1: I/O error.
sounds like a physical problem. In that case, the update may not be relevant at all. Anytime you have a disk with physical problems, the first thing you want to do is get as complete a (raw in case of encrypted disk) copy of the data as possible. This is even more critical when the disk is encrypted.
In my experience, every power cycle and read attempt can further degrade a disk with physical problems, so I typically remove power form a suspect disk until I am 100% ready to attempt recovery an then try to get a complete copy of said disk. That having been said, if I were you in this case, I would get that disk disconnected ASAP and then get another disk of the exact same size (if possible, note that I mean to the byte, not per the relevant manufacturers' marketing teams) or larger (if same size isn't possible), boot into a linux live image (or connect the disks to another machine already running linux), and use ddrescue to get a second copy of all of the data that can possibly be read. Unfortunately, taking those steps requires a bit of research, experience, or both. Moreover, if the new disk wasn't the exact same size (for a full disk encryption scheme) or the partition table isn't recoverable (for the recommended whole-partition encryption scheme), getting the data mounted in TrueCrypt will be another whole challenge that also requires research, experience, or both.
Regarding the follow-up question about the repair disk utility (with which I have no familiarity), it can't possibly do anything good for you, so don't do it. To elaborate, it might create a new partition table, overwriting your TC header, which would be bad. Alternatively, it might scan for bad sectors and mark them bad, potentially without recovering the data from them, which would also be bad. The odds of it somehow reading the problem data and relocating it without hurting any other data are miniscule if not zero.