kbrowne: While I would agree that, as a result of his exchange with Anscombe, Lewis came to believe that his formulation of his argument was flawed, the claim that he believed the argument to be fully refuted is an urban legend, which I have dubbed the Anscombe legend. Anscombe herself attributed reports of Lewis's dejection over the exchange to the psychological phenomenon of "projection." Lewis in fact produced a short response to Anscombe's argument that appeared in the very issue of the Socratic Digest in which Anscombe's own essay had appeared. In 1960, the Fontana edition of Miracles appeared, in which Lewis produced a revised and expanded version of the third chapter of Miracles, which he wrote in response to Anscombe, and which expanded on the ideas in his short response that appeared in the Socratic Digest. Anscombe thought that this effort was considerably improved, but pointed out a couple of areas where the argument needed further development if it were to succeed.
My own efforts, starting with my 1989 doctoral dissertation, through my book C. S. Lewis's Dangerous Idea and the Blackwell Companion article, has been to defend Lewis's overall argument. I think as an attempt to refute Lewis's overall argument, (as opposed to showing that it had been inadequately formulated) relies on some assumptions, popular amongst Wittgensteinians (that explaining the reasons for someone's belief can be done in a way that is completely separate and independent from the question of how that belief is produced and sustained), that most people, naturalists or otherwise, would not endorse, and which have unacceptable consequences.
It is of some interest to note John Beversluis, who is the leading critic of Lewis's apologetics, concludes that Lewis did not consider his argument refuted and did not give up apologetics after the exchange, as biographers such as Humphrey Carpenter and A. N. Wilson have claimed. He differs from me with respect to the merits of Lewis's argument, and does think it can be refuted on broadly Anscombian lines, but he has completely abandoned the Anscombe Legend with respect to the psychological impact of the exchange.