I don't know if this will comfort you at all, but I think that it is not unusual for transplanted organs to fail or never work in the first place. My dad's kidneys failed over a long period of time for still undetermined reasons (current theory is blood pressure medication). He got a transplant, but the kidney never began functioning. During this time the doctors informed him that kidney transplants are never a certainty. Sometimes they work at first then fail, sometimes they take a while to "start up", etc.
If your father does get a new transplant, I would advise you to make sure he is very cautious about his activity. My dad after the non-working transplanted kidney decided to take a trip to california. The doctor allegedly said it was ok. Being that he was on immuno-suppressants, I always thought it was a bit risky. It turns out I was right. He had to be hospitalized with a very serious infection along with pneumonia. He fortunately recovered, though it was very scary.
A couple of years later he got another kidney, and this one is working pretty well. Needless to say he didn't take any trips for a long time. It's hard for me to imagine what it would be like with liver problems. It's scary and troubling enough with kidney problems, which can be controlled via a couple of dialysis options.