What social issues can be found in "A Rose for Emily" that made Emily isolate herself from the outside world?

There are several social changes that occured within Emily's life.

The society that once witnessed old-fashioned courtships, kinships, old family names, an economy by means of hand labor, and the perennial presence of the Southern way of life is, in the story, now steadily shifting towards industralism, capitalism , social expansion, racial integration, and the view of the South as anachronistic. 

Emily is there, caught in between the two clashing worlds, without the protection of her "almighty" father, and with no ties that are strong enough to help her make the transition towards the present.

The social issue in itself is the inevitable reality of change and shifting towards the future by severing the only ties you know. This is a universal problem that happens in every generation, and needs the willingness of each individual in it to make the effort and embrace change.