The browning of foliage on aster is likely due to a fungal leaf spot disease. In moist conditions especially, asters can be susceptible to foliar leaf spots. If the plant was weak to begin with, this may push it over the edge, but normally plants regrow again next year. However, it's also likely that the disease will reoccur next year, too. Remove all aboveground plant material from the aster this fall and destroy it to cut down on overwintering fungal spores. Consider spraying the plant next spring with a fungicide to prevent the disease from getting started.