Answer: Based on your description unfortunately I am not able to diagnose the problem for you. Impatiens flowering is sometimes affected by mites which can be treated with insecticidal soap, however if this is the cause you would most likely also see some distortion of the foliage as well. I would suggest you also consult with your local Cornell cooperative extension to get a more specific diagnosis and based on knowing that, decide how to proceed. In the meantime, although it sounds like you are probably already doing this, make sure the impatiens are growing in bright dappled light or a few hours of direct morning sun at most, and that the soil is evenly moist (not sopping wet and not dried out). Lack of water can sometimes cause the buds to drop without opening. I'm sorry I can't be more specific for you.
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