Ran short of water?
Flowers are past their prime?
Low humidity?
Windy weather?

Please post a picture of the plant.

Here's a picture of a flower with brown edges. Even some of the buds have browning. Has not been deprived of water. Has not been windy. Plant faces east and gets morning sun.

Hard to tell for sure from the photo, but ovulinia azaleae, also known as petal blight is the most likely cause. Periods of high humididty and/or overhead watering are contributing factors. Best to pick off the blossoms and dispose of them. Replacing any mulch that may harbor spores is also a good idea. There are several fungicides listed for this disease, but they are all preventative rather than curative.

The azalea does not look like a rebloomer, hence it should not be blooming now. Azaleas bloom in the spring. When they get blooms in the fall, the blooms are poor, incomplete, and not worth worrying about. It is freakish behavior and is more prevalent on certain varieties, in certain climates, and during certain years.

Petal blight gets worse as the blooming season goes on. This fungal disease, caused by Ovulinia azaleae, primarily affects the flowers of azaleas, but mountain laurel and rhododendron flowers can also be infected. Indian and Kurume azaleas are especially susceptible. The disease starts on the flower petals as tiny, irregularly-shaped spots, giving a "freckled" appearance. On colored flowers the spots are white, and on white flowers the spots are brown. The spots quickly enlarge and become soft and watery. Flowers rot and stick to the leaves. Infection is easily spread from flower to flower by wind, rain and insects. The fungus survives the winter in the soil. The most important things that you can do to control this disease in the home landscape are to pick and destroy infected flowers and avoid overhead watering. This fungus survives in the soil, so it is important to replace the ground litter with uncontaminated mulches. Rake and remove flower debris from beneath plants and, if possible, remove old flowers still attached to plants. Apply new mulch around the base of plants to serve as a barrier to new infection. On large azalea plantings, where it is not practical to remove infected flowers, make weekly fungicide applications beginning just before bloom and continue until the last buds open.