It's not uncommon for the N.C. Cooperative Extension of Craven County office to receive questions about tiny, developing young grapes falling off the vine in the spring.  What's usually happening is that these are female flowers that aren't being pollinated adequately, so they eventually fall off the vine without developing into fruit.  Or perhaps more commonly, a vine that is all or mostly male flowers, so there's no chance of fruit development.  I suspect that in most cases it is in fact the latter, because there are so many wild muscadine vines in the region that an all-female vine such as 'Scuppernong' has at least some chance of being pollinated by a nearby vine in the woods or landscape.  (Or the neighbor's property).  By way of comparison, see the images below of unopened flowers in May vs. developing fruit in June.