From your description, I am guessing this is a potted florist azalea, probably indoors.

They are killed more often with kindness than sunlight. The main killer is water. They need well drained soil. There must be a drain hole in the bottom of the pot and they should not be watered too often. They soil should be nearly dry before watering. I judge that by lifting the pot. When it becomes light, it is ready to water.

You shouldn't water with water from a water softener. It is high in sodium and azaleas don't like sodium. If you have a water softener, then use rain water.

If the pot is still light after watering, you may need to soak the pot in a tub/bucket of water for about half an hour to get the soil thoroughly soaked. Once the soil dries out, it is hard to get it to accept water again.

They don't need much fertilizer. Whenever using any fertilizer, never use more than half the amount suggested on the package.

Azaleas are typically an outdoor plant. Unfortuantely most of the florist azaleas tend to be too tender to be planted outside. You didn't mention where you live and what the variety the azaleas is.

I am having the same issue as the original poster. I have this with 3 out of 7 of my Encore Azaleas facing east.
I am wondering if I should cut the shrub back to remove the brown leaves? I did water mine but will ease off the watering for now.

Any other advise?

Thank you ,
Sharon

Feel free to prune dead tissue now, keep 3-4" of acidic mulch and try to maintain the soil constantly moist as much as possible. The windy hot summer days here tend to cause a lot of evaporation on the top few inches of potted soil (or top soil) and that is where the azalea roots are found.