(The following post should not be misconstrued as expressing a lack of respect towards Rav Shlomo Zalman Auerbach, ztz"l. I lived around the corner from him for several years, spoke with him on a few occasions, and I have tremendous respect for him. He was justly renowned not only for his incredible knowledge, wisdom and saintliness, but also for his breadth and open-mindedness. Yet "open-mindedness" is a relative term, and he was nevertheless a product of the charedi world.)
In Shulchan Shlomo (vol. III p. 24) it records that for a long time, Rav Shlomo Zalman Auerbach categorically rejected the notion that brain death constitutes death. His reasoning was based on the Gemara in Erechin 6a, which states that if a pregnant woman dies, there is no chance of survival for the fetus. With a pregnant woman who suffers brain death, on the other hand, the fetus can survive. Hence, Rav Shlomo Zalman deduced, brain death is not death.
Yet there is no basis for this derivation. One simply cannot draw any inferences from this Gemara to brain death, which is a radically different scenario from anything that Chazal could have had in mind. When the Gemara says that a dead woman cannot deliver a live baby, this was merely describing the reality of 1500 years ago and it surely has no bearing whatsoever on the modern question of whether brain death is death. The fact that Rav Shlomo Zalman drew such inferences demonstrates how Poskim are accustomed to drawing halachic conclusions from the Gemara even when there is no reason to do so - i.e. when the Gemara is not remotely useful in addressing a novel, modern situation.
Now, some people at this point will be hopping mad, and will be wondering how I could possibly be so brazen as to say that Rav Shlomo Zalman was using the wrong methodology. But he eventually admitted it himself! Shulchan Shlomo notes that this was after being presented with the report of an experiment in which a pregnant sheep was decapitated and its body maintained with a respirator. The baby lamb was successfully delivered via C-section. Everybody agrees that a decapitated sheep is dead, and yet its baby survived. Rav Shlomo Zalman therefore noted that today, we have the ability to maintain certain bodily systems even in the absence of others, and thus Chazal's criteria no longer apply. He thus acknowledged that he had been mistaken in thinking that the Gemara about a pregnant woman's death could be used to resolve the contemporary question of brain death.
Rav Shlomo Zalman's own eventual conclusion about brain death was that although complete cellular death of the entire brain is indeed considered death, brain-stem death does not clearly qualify as such. However, the point that I want to bring out is that even Rav Shlomo Zalman made the mistake of using a traditional, Talmudic-halachah based approach, when others would have recognized from the outset that this is entirely inappropriate in such a case (as did I, as soon as I read about Rav Shlomo Zalman's deduction from the Gemara about a pregnant woman, even before I discovered that he retracted). It is especially significant that it was Rav Shlomo Zalman who did this - as I noted last week, Rav Shlomo Zalman himself acknowledged that there are no precedents in the Gemara for drawing halachic conclusions about cloning. But his recognition of that with something as novel as cloning did not mean that he recognized it as also being the case with determining the moment of death.
It is unfortunate to have to draw attention to the error of such a great person. But such misguided approaches to resolving the question of brain death are, tragically, all too common - and since it is a matter of life and death, it is important to be aware of the tendency to make such mistakes.
UPDATE - I just read the discussion of Rav Shlomo Zalman's view in the RCA document. They stress that there was no retraction on the halachah of brain death, just a withdrawal of one of the arguments that he formerly presented. The impression that I received from Shulchan Shlomo was quite different - that this was his primary argument, and that as a result of the sheep experiment, he modified his view somewhat from categorical rejection of brain death to stringent concern that brain-stem death might not equal complete brain death.
Furthermore - and most significantly - the RCA document suggests that due to various reasons, the sheep experiment is not analogous to the Gemara's case, and that cases where pregnancy continues despite brain death caused by stroke or cancer are analogous and do indeed demonstrate that brain death is not death. But this is exactly the same sort of mistake that Rav Shlomo Zalman admitted to making. The Gemara is not talking about a case of a person who is brain dead and has their body maintained via a respirator - such a situation was beyond the imagination of anyone back then, and no inference can be brought from the Gemara for such a case. One can make a reasonable argument that the fact of a brain-dead woman being able to grow a baby within her indicates that brain death is not death - but one cannot draw this conclusion as a halachic inference from the Gemara.