Hi there. I have been fighting this same problem for four years in a row myself. From what you describe, and what I have myself seen on mine, it sounds like Black Rot, a fungus infection of the vine and the soil. There are a couple of pictures at this location to see if it matches what you are describing. It is the first entry on the list:
A good fungicide applied when the leaves first develop, a few weeks after the fruit set, and midway through the growing season does well to control it. The most important thing, I have discovered, is picking off affected fruit showing any signs of the fungus and disposing of them well away from the vine, as well as removing any ruined fruit on the ground in the area of the vine. The shriveled fruit are carriers of the fungus, and will continue to contaminate the vine and soil if left.