I have an alternative explanation on why taking breaks can be beneficial. I'm less of a fan of the subconscious theory--it can certainly happen but I think it's much less common than people estimate.
What I think is more likely is that you get fresh insight when returning to a problem after a break, because the mental model that was constructed in your head was subtly wrong. It's happened to me a bunch of times: "OK, where was I?... the grommit plugs into the foobar, and the whatzit sends a message to the widget... wait a minute, no it doesn't, it sends to the frobnosticator first! WHY on earth was I thinking that for all that time before the break??"
Sometimes it's as simple as the famous case of getting somebody else to look at your code and immediately point out what's wrong that two hours of staring at the screen couldn't accomplish.
Other times it's a lot more subtle, high-level and abstract. Since, in those cases, it's often difficult to discuss the problem with somebody else, you don't get a) the outside feedback to speed things along and b) the humiliation factor that makes you remember how the insight came about. ;) So the meta-revelation of how you came to that revelation might be lacking, and it's attributed to the subconscious instead.