All plants have a finite life span (though some, like bamboo, seem immortal because they are colonial). There are azaleas that are over 100 years old, but depending on the type of azaleas that you have and the conditions they are growing in, senescence could be setting in. Senescence diminishes a plant's ability to deal with environmental stress. The actual cause of death may have been heat stress, dessication or freeze damage, but the plants were able to tolerate these adverse conditions better when they were younger. Perhaps you just have a number of senescent branches that need removal. Sometimes cutting a plant back hard can help rejuvenate the plant with new tissue in which cell division is vigorous and will remain so for many years. Azaleas generally respond well to pruning. Try cutting one-half of a plant back hard and see what it does. If that doesn't work, you'll have to replace them. You still got a good return for your initial investment of a few dollars back in the 1980's.

Thank you, Dick_Sonia. Good advice!
Alice