Every year, but this year, I have had my two Rose of Sharon plants blooming beautifully. This year, there is only one flower on one bush,and half of the plant looks dried up. Too much rain the Summer?

We have had several conditions this summer that have caused plants to not perform as expected. It started with the drought of 2012, a better but not stellar 2013 and then the extreme winter of of 2013/2014. Your plants have likely suffered root loss from the drought, the winter likely caused die-back in the crown and stems from freezing and killing cambium cells. While plants started out ok, you are now seeing the damage. Prune away any dead branches as they are non productive and could harbor additional problems. Make sure the plants are well watered going into winter and hopefully the remaining plant parts will generate additional buds.