The first reason magical beliefs continue to exist is it feels good to believe in them. It’s a sort of mental stimulation when one thinks there is something magical out there that can’t be explained that is going to show ‘them’ that they’ve been wrong all along.
It’s pleasing to believe that you know of some alternative medical practice that, while irreproducible in science, miraculously heals people while tens of thousands of physicians worldwide ignore it. These things don’t have to be medical, they could even be knowledge of a ‘magnetic’ hill where cars in neutral roll UP hill instead of down. Magic!
The second reason is that once a person buys into many of these beliefs their ego prevents them from deviating from this line of thinking. This is especially true if fundamental religious beliefs tie into these belief systems. Don’t get me wrong, I’m certainly not knocking religion, but in the case of faith healing (I’m talking about the televangelist type of money-grubbing stuff) there is a familiar thread of magical thinking involved.
For me, there's another reason - the inability to differentiate between a valid scientific evidence, versus anecdotal evidence. They don't know the criteria on what constitute a scientific evidence, and WHY we have such criteria.