I bought a house that had been sitting for some time. One of the the issues that I've discovered is that the flapper valve leaks. I've come to this conclusion by turning off the water to the tank and combing back later to see that the water level is lower.
I have already replaced the flapper valve itself, and the leak remains.
Best Answer
Over time the surface of the plastic part that joins the tank to the bowl can get tiny defects in it that prevent the flapper from making a good seal. As Jeff suggests, you could try cleaning that part, or just replace it.