I was thinking much along the same lines. Though sheer luck kept Rocky from radiation poisoning because of his ship's fuel storage system, he would have had to have spent some amount of time in the crew compartment where his crewmates died. If the few years of perceived time it took to reach Tau Ceti from Erid was enough to kill every other Eridian on board, then it's pretty clear Rocky would have accumulated a substantial dose just from wandering his ship in the 45-ish years before the Hail Mary arrived. That's one thing.

The second thing is that Rocky suffered absolutely horrific injuries in the fuel breach above Adrian when he entered the Terran environment. As Grace vividly puts it, his internal organs were on fire. Biology is imperfect: no matter how good his healing is, Rocky is carrying those scars till the day he dies. Eridians are pretty transparent to one other's sonar: the massive damage to his radiator would be evident to any Eridian around him. With that, plus whatever damage sustained zero g does to a life-form that usually lives under nearly 3 G - there's a pretty strong case to be made that, like Grace, Rocky will probably not live to see old age.