Great question. We know a little bit about the neural correlates of attention itself: when you’re very focused, some neurons are firing more than usual. You experience increased blood flow to prefrontal and parietal areas.
Attention relies on a process called working memory, which (we think) involves neurons actively firing to maintain a representation of the thing you’re trying to remember. Some theories suggest that when we try to learn something, it moves from working memory into short term memory and then into long term memory, and each of these has associated neural changes.
Why those neural changes can only support a limited attention span, though, is less clear. It could be a computational problem—that our neurons are only capable of maintaining x amount of representations, and once we hit that limit information needs to be moved into long term memory or it’ll get mixed up with the other representations. Or it could be a physiological limitation—the neurons run out of “juice” and can’t keep firing at the enhanced rate. Or it could be a motivational problem—maybe nothing has changed in your brain, but you’re bored and you just don’t want to study any more.