So I just read this PBS author interview which tries to put some reasons to it: http://www.pbs.org/wgbh/pages/frontline/countryboys/readings...
The main takeaway, as I read it, is that in cities and other rural areas there is a middle class and even some upper class folks around and the resources they bring along (and maybe even the example they set... sorry if that's offensive) is a positive influence on the extremely poor. In cities, obviously you have better municipal services and programs and a professional class of doctors, lawyers, etc. In rural farmland many families own their land which has some value and there are some wealthy landowners with large tracts sprinkled in.
In Appalachia, there's none of that. The land isn't worth anything and it's just poor poor poor as far as the eye can see (which is large, geographically, unlike inner cities).
Except for coal mine owners and operators. That, I can't explain. Do they live in the area? Do they not contribute to the communities? The PBS article goes as far as to say they actively held the poor down to keep them working in the mines, but I'd have to see more evidence to believe that wholesale.
In any case, it strikes me that this wasteland of poverty with very few middle class or wealthy folks is the opposite effect of tech hubs. Brad Feld and others have written about how the density of entrepreneurs and angel investors with deep pockets is what makes a tech hub viable (very liberally paraphrased). From a general perspective, it seems like a normal curve where the outliers at the top are places most uniformly non-poor and populated densely and the outliers at the bottom are uniformly poor and populated sparsely.