It seems that the GOP is simply better at turning out their voters than the Dems are. In a tossup race, it's usually the side with the better turnout operation that wins it. Other than Obama's two wins, Dems have probably not won the turnout war since 1992 or earlier.
I don't think it is so much about being better at turning them out than it is about Republicans counting some of the highest turnout demographics as part of their base. Old people, the wealthy and well educated are all naturally high turnout voters and also currently Republican-leaning. Meanwhile, Democrats rack up huge margins among minorities and young voters, both of whom generally have some of the lowest turnout rates.