It is unconfirmed whether he is dead or not. There are many versions:

1. His Arwing was shot down on Venom and:
a)He was captured and tortured to death.
b)He got away from the crash site and is surviving on Venom.
c)He got away from the crash site and hijacked a Venomian Striker and saw that Andross could only be defeated if Fox believed he was dead and changed his identity (This explains why he only occasionally appears in the later games).

2. His Arwing was sucked into a black hole and:
a)Was sent into the Solar System
b)Was sent to an alternate dimension where the Starfox team were evil.
c)Was killed by the gravitational pull of the black hole.

Though in Starfox Adventures it seems he is dead. When you put one of the cheat tokens in the cheat well it says that it is a message from a long departed friend and has James saying something along the lines of "I am so proud of you my son"

I really hope he isn't dead though.

Yeah i hope he isnt dead either, because on the Star Fox 64 on Expert mode after u defeat Andross, James Comes out and you have to follow him on the way out of the venom tunnel. So it could have either been his ghost or that he was alive. who knows???

i hop e he is not dead because fox then would not give up and maybe one day fox will find him!