There are three possibilities where you might find individual branches on azaleas dying -
Plants that are experiencing drought will sometimes react with entire stems or branches dying instead of the whole plant - almost like they are conserving what little moisture there is by making a sacrifice :)
Rhododendron/azalea borer (insect), and bark split which is weather related. Sudden low temperatures in Fall or in early Spring after a warm up can cause bark to crack and separate from the body of the stem and the branch beyond the stem will die.

Thanks for the info. No problem with drought and I checked the dead limbs for a borer. I would say the weather but they were doing it last year.

There are two other possibilties that I know of.

1) overly wet soil can cause roots to die

2) Phytophthora root rot. Phytophthora is a soil-borne fungus-like organism that attacks roots.