Environmental stress can cause impatiens to wilt, or appear to be dying. They also drop leaves and flowers. To prevent this, make sure you're watering enough. Keep the soil moist but not boggy.
According to PennLive, impatiens are fairly susceptible to root rot diseases. If your soil contracts a fungal diseases (and there are several types out there), your impatiens' roots will rot underground. Above ground, the plant will die back. The only fix for root rot is to remove all of the soil from the area and replace it with clean soil, or to plant flowers that don't succumb to this disease.
Cutworms can infect an impatiens patch and kill the flowers. These plant pests will nibble the stems, which causes the impatiens to wilt and die. To get rid of the cutworm, you'll need to use an insecticide that's approved for your area. Planting impatiens in containers with fresh soil will ensure they're safe.