Well, when your mind is made up you can explain anything - perhaps the autism is a punishment for not trusting in the original protection, etc, etc

Indeed. If you want talk to them with their terms, you might have better luck with "God helps those who help themselves", though I doubt that will work in practice either.

Sure, but it's not like they're consistently anti-medicine, happily 'helping themselves' to cancer treatments and the rest (well, except for the oddly named Christian Science sect, but not the broader Bachmann-style evangelicals that are found overlapping with the anti-vaccine movement these days). It's almost like existing biases helped them succumb to the original fraud and helped them get stuck in it, so now they just truly believe that most medicine helps but vaccines cause autism. Fortunately it doesn't seem to be spreading across evangelicals as a whole.

That's a legitimate question, and I don't pretend to have an answer. I believe God has healed in numerous cases that defy explanation by placebo, misdiagnosis, or other means, but that tells me little about why he has not done so in others. I could come up with theological theories, but none, at least presently, that I would expect others to find satisfactory. It is also, I admit, not a question I have specifically spent much time considering or investigating, - - though I acknowledge its difficult implication.

Fair enough. I used amputees in my example because they were the most obvious, but there are plenty of afflictions that prayer never cures: Down syndrome, spina bifida, cleft palate, Tay-Sachs, dwarfism, etc.

I hope some day that you have a satisfying answer to this question.