No, Your Azalea Isn't Dying
People expect to see green leaves on their outdoor plants. It's a sign of life and good health. Thus, when you discover one winter morning that many leaves have turned yellow, you're apt to conclude said plant is headed for That Big Compost Bin in the Sky.
This is especially so if your "ailing" plant is an evergreen. Evergreens have green foliage year-round, right? Not exactly. Individual leaves don't live forever. Most last one or two growing seasons and then die and drop. The difference between deciduous and evergreen plants is that the former drop all of their leaves each year at once, while the latter space out the time that they do it.
Why do leaves of evergreens die if the plant itself is healthy? Consider the purpose of their leaves (or needles). Their two main functions are to turn sunlight into food and then store that food. Young, fresh leaves do this quite efficiently. However, the older leaves get, the less efficient they become due to damage from UV radiation, wind, heat, cold, drought, pests, and other things. Therefore, the plant decides they're more trouble than they're worth, lets them die, and replaces them with new leaves. Quite logical.
Older leaves are the "inside" foliage of the evergreen's twigs and branches, while new leaves grow near the tips. That's a good way to tell if yellowing, dropping leaves is a positive or negative sign. If all the yellowing leaves are found towards the interior, no problemo in most cases. However, when lots of new leaves at the tips turn yellow, you should be concerned, because something ain't right.