Answer: Based on your description I am not certain what is happening to your azaleas and rhododendrons. It is possible that the overall location is just not suited to these plants -- in addition to specific soil requirements, they also do best in morning-only sun or bright dappled light all day, avoid full sun, afternoon-only sun and windy sites.
It is possible there is an underlying problem such as a tree root (black walnut will kill these outright, but black locust also has some allelopathic qualities; tree roots often extend more than twice as far as the branches spread) or there may be a soil problem.
These plants require a well drained site where the soil is organic, humusy, acidic and evenly moist like a wrung out sponge. If grown in unsuitable soil they are weakened and more subject to disease and pest problems or will die outright.
Also, there are some diseases that are carried in the soil and can also be carried on tools from one plant to another. If this caused your earlier plants to die, then the replacements would also be affected.
The description of branches turning white is not a clear match to the typical problems on these plants. Powdery mildew can cause a white powder on the foliage, but would not usually kill the plant outright. Winter damage can cause the foliage to turn very light brown or gray, but I would not describe it as white, for example.
I would suggest you work with your local Penn State county extension to obtain a more specific diagnosis of the problem and based on knowing that, determine what to do next. I'm sorry I can't be more specific long distance.
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