Don't worry about something you can't control - everyone and everything dies sometime, it's what makes life so precious.
But Jimby isn't that old, he's a small/medium rabbit - when neutered and healthy they can live to 12 years. Middle-aged is just that, in the middle, he's got nearly half of his life left to go.
Barney is also a minimum of 6 years old (very likely older, his age is unknown), he is a large rabbit (shorter lifespan), very underweight, has chronic snuffles, has chronic gut problems, has a really bad infection in both inner ears, has arthiritis and bad back problems/injuries and is on 6 medications daily, two of which are painkillers. I am going to be devastated when he passes, and every winter I think he's going to go, but you know what? Every spring he's still here. If Barney can keep going despite all of this, I'm sure Jimby will be fine.
Be positive, 6 is just a number, and not a very high one. 6 years old is not a death sentence, that's like saying humans all drop dead at 55. Don't worry about something you can't control, just focus on the present, and yours and Jimby's happiness.