John Scotty Edmond wrote:

Last summer one Azalea started dying, one branch at a time, slowly
spreading over entire shrub. We had a rough winter here in NJ, and I
just saw the same thing happening to another Azalea, located a
distance from the dead one. This shrub was healthy in autumn,
apparently this developed during the winter. The leaves are dying,
some leaves half green, half brown. Please see attached photo.

This sounds like two different problems.

1) one branch at a time is usually due to drought. The plant struggles
to survive by shutting off one branch at a time and trying to keep the
others alive. If it progresses, the entire plant dies.

2) a leaf that is half green and half brown, it appears to be winter
damage. It could be a combination of drought damage and winter damage.
The drought stressed the plants severely. The winter then added more
stress. The dying leaves are probably the ones most exposed to the
winter sun while the roots were frozen. If you are in a sandy area of
NJ your stress could be more severe.

The second plant should survive if properly taken care of.

--
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Cheers, Steve Henning in Reading, PA USA http://www.users.fast.net/~shenning