Crankery in old age is really sad. (And, weirdly enough, the topic of the latest SMBC strip.) I've wondered sometimes about why this happens; it seems to correlate with age but not young or middle age, so I discard the default hypothesis that a false idea finally got lucky and slipped through one's memetic defenses (since that feels like more of a Poisson distribution).
As you age, your general intelligence takes a real beating but your personality traits like Openness don't change so much (and great scientists will tend to be very Open). Openness and low IQ is also correlated with being New Agey crap and that sort of thing (IIRC, citations in Miller's Spent), and these bizarre false theories do seem New Agey in some respects ('it's all, like, circles of energy man!').
Could this be the problem? When you're young and sharp, you can keenly examine new theories and ideas, although you have the handicap of being ignorant and not having spent much time on matters; so your productivity rises in your middle age to your early 40s; but by that point, your raw intelligence has become blunt and dull, and your knowledge may be increasingly out of date, while your interest in new ideas remains the same. So you continue to seek out or look at new ideas, while you are no longer able to evaluate them.
So to test this we'd want to test the following:
Check the New Age <-> high Openness/low IQ correlation
(If it doesn't hold true in unscientifically capable or trained populations, why would it hold true for old eminent scientists?)
Test that 'weird and false ideas' do disproportionately pop up in old age
(as opposed to being adopted as impressionable grad students but only worked on & espoused in the leisure of old age/tenure/retirement, or following some 'lightning strike' model, due to say the simultaneous occurrence of emotional trauma and a meme impression)
That their rate does correlate with being Open
(If there is no such correlation, it may be that the entire effect would be IQ-related.)
That their rate does inversely correlate with IQ at that time, ideally, at the instant they accepted the false idea
(If it turned out the acceptors of false ideas had most of their IQ intact, and the more conventional ones were stupid, this would be rather odd.)
Come to think of it, compartmentalization effects (like with religion) might allow one to be brilliant for a while until the disjoint beliefs finally interact. Were the physicists who became cranks eventually ever particularly good at dealing with the flaws in reasoning of crankery while they were still respectable?
Similarly, it's possible that as they became more prominent, they needed less and less to justify any given statement to the people with which they interacted, having gained more and more authority, and thus just lost socially enforced habits o...
Freeman Dyson writes in the New York Review of Books about people who took up the crackpot offer. Not just complete cranks, but eminent scientists such as Eddington who got into crankery in their later years.
New thing I learnt: Dyson was not only a good friend of Immanuel Velikovsky, but considers him a greatly underappreciated poet.