The usual reason for this is lacebug infestation. The insects are very hard to see, but generally the underside of the leaves will show shiny spots which are often likened to varnish. The entire leaf is usually affected, but it may be that the leaf tips are thinner and therefore show the damage more readily.

There's nothing to be done at this point for this year's leaves. There's a great deal of information on this site and elsewhere about prevention of lacebug damage for next year.

That looks more like chlorosis - pale leaves with darker green veins.

The most common cause is soil with too high ph which leads to iron (sometimes magnesium) being unavailable to the plant. Local water can also be alkaline or of too high ph, compounding the problem.

However, anything that could damage roots, leaving insufficient roots to supply the plant with needed nutrients, can lead to chlorosis too. Nematodes, poor drainage.

Do you have any idea of your water PH, and what kind of growing medium do you have in your container. Potting soil/container medium needs to be high in organic material but fast draining. Unlike azaleas in the ground, container grown plants will need to be fertilized....

No lacebugs, no varnished or shiny spots on underside of leaves. However, our gardener did leave this plant sitting in a puddle of water for perhaps a couple of days. I removed it and gave it some acid and iron and it looks a tiny bit better now. Yes, our water tends to be alkaline, causes problems with our pool and algae as well. This particular azalea is in a packaged mix of earth, has been for a year or so, was doing great until the over-watering and the intense temps of summer began -- up to 105. We do fertilize it in spring, too hot now.
Another azalea bought at the same time but kept in a more shady area has no problem, that's why I thought sunburn might also be a cause.

Yes, sunburn. Protect it a bit with some shade until the soggy roots recover.

Unfortunately, drying out the roots, putting it in semi-shade and giving some soil acidifier has not solved the problem. Leaves continued to go yellow->white->dried up brown. Plant dying, probably something eating the roots. May have to repot. Same thing happened to two other azaleas last year.

Although some leaves appear to be suffering from iron chlorosis, most of the green leaves are not affected which is odd and may hint at a mineral problem. I would try to get a soil pH kit to confirm if there is a soil pH problem. Also get a soil test kit to check the N-P-K Levels (too high or too low). Root problems can result in soil pH problems sometimes too.

It can take several weeks for a high pH problem to be fixed. It does not correct quickly. But using iron-chelated liquid compounds does speed things a bit when compared to non-liquid amendments like garden sulphur, iron sulfate, green sand, etc.

I would also add some liquid seaweed -which usually contains a very small amount of NPK- to provide the shrub with trace minerals in case there is a lack of them.

Too much sun: this will make the area near the central leaf vein turn yellow first and then extend the yellowing to the rest of the leaf.

Last suggestion... make sure the fertilizer and amendments that you use does not contain aluminum as this is toxic to azaleas.