Hark. They are on an automatic drip watering system. I will keep reading but that sounds like the problem...

@tete_a_tete, the root mound is pretty moist. It looks like it had plenty of peat in it from the nursery, and that might actually be part of the problem. These plants like moist but fast draining soil and this might have gotten too dry but now might be too moist from my overwatering? I tried to peal off that peat so I could replant the roots in sized fir bark, but it is very compacted material.

How often should I be watering this plant, now that I am sure the soil is moist?

The plant continues to decline.

So the azalea that went without water continues to deteriorate. The rootball has peat and feels moist so I don't think it lacks water. If anything, I might have overwatered once I found that it was dry. Look at the next two photos. The first shows the affected plant. The second photo is the identical species right next to the affected plant, and as you can see it is thriving. It is on the same drip irrigation system, and it came from the same nursery at the same time, so you would assume it has the same soil.

Notice how the large leaves all shed off, and the small leaves are getting brown in the middle, but stay green at the tips and base. Does that give any clues?

Alla the signs point to a water shortage. That can come from a dry planting mix or rotting roots.

Did you ever submerge the rootball in a bucket?

If not, and if the plant still has some green, please do it, in spite of what the peaty stuff feels like.

Or did you tip it out of the pot to look at the roots?

I submerged it, and a few days later I took it out. The rootball is moist. I don't think the plant lacks available water.

Assuming the roots are rotting, what can I do?

How often would you be watering this plant, under either scenario (a) it was underwatered and b) it has root rot)?