dreamsunderstars: I don't know about them being marked for death if they got disconnected and went rogue. The hive mind would just assume that it got killed. The only way it would know if the illithid was still alive is if they encountered it. And astral space is infinite.
The disconnection theory is a plausible one, but as LawfulStupid says, it's quite likely that such an occurrence would drive the illithid to near-madness and fill it with an obsession to return to the hive mind at all costs. For illithids, the constant, omnipresent presence of the Elder Brain is like a warm, reassuring blanket. (In the Lords of Madness supplement, it's revealed that illithids who leave the community for extended periods often bring along psionic items that mimic this constant telepathic chatter.) For a human, the equivalent of losing this constant contact with the Elder Brain would be like being suddenly struck blind and deaf, able to sense the world only through smells and touch. You could still survive in such a state, naturally, but how impossibly lonely and isolated would you feel?
There isn't a lot of lore about alhoons (illithid liches), so we know very little about what would motivate an illithid to embrace undeath. While the transition to undeath does not rob the alhoon of its psionic powers (and the ability to telepathically communicate with others), it DOES mean that they give up any chance of ever joining the Elder Brain upon their deaths, which would be like a human voluntarily deciding that they never want to enter heaven after they die.
Of course, there is ONE possible reason I know of, which is that the Elder Brains lie to their children about what this union means. Illithids believe that their individual consciousness survives when their brain is ceremoniously removed after their death and placed into the Elder Brain's pool, but this is not true. All of the illithid's memories will be assimilated into the Elder Brain, but the illithid itself is gone. Only the Elder Brain lives forever. Perhaps alhoons have discovered this, which is why they chose the path of undeath. (Curiously, if any alhoons do know this truth, none of them have ever seen fit to speak the truth to their illithid fellows.)
Addendum: Of course, it's also possible that while the illithid's individual consciousness does not survive the merging with the Elder Brain, we simply cannot grasp what it truly means to become part of a gestalt intelligence. Perhaps individuality is a totally irrelevant factor when compared to the ascension that becoming part of a greater being entails.