Answer: It can be very difficult to grow azaleas in a container under home conditions. I am not sure why you have it in a container, it probably would have been less stressful on the plant to have planted it last spring so it would be well established before winter sets in.
Azaleas are sensitive to over watering, underwatering (they need soil that is evenly moist yet well drained meaning like a wrung out sponge, not saturated sopping wet and not dry), and salts build-up from overfertilizing or from a household water softener. The soil should be acidic, humusy, and organic so it stays evenly moist yet well drained. They also need a location in bright morning sun or bright dappled light all day as well as good air circulation.
Ordinarily wilting would be caused by lack of water, however in a container situation it is sometimes caused by overwatering, or by soil that is not draining well, or by leaving the container sitting in the drainage saucer with excess water in it. Overwatering can damage the roots which then leads to foliage symptoms. To know if you need to water, dig into the soil with your finger. If it is still damp, do not water yet. When you do water, water thoroughly and slowly so it soaks into the soil and does not run out between the soil and container.
Sometimes azaleas suffer from fungal infections and other diseases and browning/wilting despite correct watering can be a sign of that. I would suggest you consult with your county extension and see if they can diagnose the browning for you and then knowing that, help you decide how to proceed. If it is something that needs a chemical control, they will have the most up to date information on what to use and how/when best to apply it. Good luck with your azalea!
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