The main problem is that the population in question is never rigorously defined, and the working definition is vague and constantly shifting. That's understandable in research on gifted because researchers are education people concerned with practice and equitability, not scientific psychologists trained in cognitive development. In ASD, research attempts to find "the explanation for ASD" against a shifting pattern of PPD-NOS, Asperger's, and other diagnoses.
With savant syndrome, the vagueness increases exponentially. It doesn't help that the terminology has changed. In the early 20th century, there was "idiot savant," which was inaccurate and demeaning. After Rain Man, there was "autistic savant," which obscured the fact that many savants don't have autism. Both terms were replaced by "savant syndrome" recently, probably thanks to Darold Treffert.
The variety of talent--each of which probably has a different neural basis in neurotypical people--is astounding. There are artists and musicians (all with perfect pitch, some composers and some performers with perfect memory for pieces they heard once 40 years before). There are calendar calculators, who can tell you what the day of the week was on a certain date. There are math geniuses who can find prime numbers of 8 or more digits or factor large numbers in their head. There are polyglots who can learn a language in a week, people with perfect time sense, prodigious memorizers, people who can measure accurately without instruments, and more. Basically, if someone with a nonverbal learning disability is likely to be bad at it, a savant is likely to be good at it. Some believe people with hyperlexia are also savants because they have good mechanical abilities with language but little comprehension; this is more controversial. Only the most general similarities link these skills. All of these talents could be loosely called "right brain." They have been (falsely) called nonsymbolic. (Math is clearly symbolic, as is music to a lesser degree. Calendars aren't exactly symbolic, but they're highly structured). It's hard to believe there can be one cause for all these talents, but of the more than a dozen articles I've read in the past couple weeks, every single one has proposed one single explanation for all of savant syndrome.
Worse, most of these explanations aren't savant syndrome-specific. They tend to be explanations of autism imported over wholesale, on the assumption that savants are all autistic. (This is a misconception probably created by the movie Rain Man--in fact, only about half of savants are autistic). So we see the same, somewhat annoying theories about weak central coherence, detail-oriented processing, etc., most of which have only the most tenuous connection to savant abilities. For instance, none of these theories have anything to do with memory, but every savant has higher memory than others with the same IQ, and many have memories that would be impressive in a neurotypical. For some, like Kim Peek, the memory IS the talent. As far as I know, while there may be minor memory differences between people with autism and neurotypicals, memory differences are NOT a key symptom of autism. And yet, in my literature search, almost every article seemed to look only at autistic savants, use autistics who were not savants as control groups, apply a theory about autism to savants, and/or just cite a lot of literature about autism.
Consider the differences between Kim Peek, the inspiration for Rain Man, and Daniel Tammet, known for reciting pi to 22,514 places. You can see their brief encounter here. Kim has intellectual disability and lacks a corpus callosum; Daniel believes he owes his talents to synesthesia, possibly caused by epileptic seizures as a child. Daniel has come up with an intriguing explanation for his abilities (in the most recent Discover magazine, I believe), but I'm not sure how well it applies to Kim. Similarly, a theory designed to explain Kim (not that I've seen any) might not cover Daniel.
A discussant at a 1964 meeting of the APA said that the importance of the savant "lies in our inability to explain him; he stands as a landmark of our own ignorance and the phenomenon of the idiot savant exists as a challenge to our capabilities" (Horwitz et al, 1965). Despite our advanced neuroimaging techniques, that seems to be as true today as it was then.