Answer: New growth on these plants is often quite soft and tender. The drooping is fairly typical, especially if they have been fertilized generously. By the end of the season the lower part of the plant will become woody. Butterfly bushes are grown as cutback shrubs in your area. This means they are cut back close to the ground early each spring. This removes any winter killed branches and also stimulates branching low on the plant, it also helps keep it a bit smaller and neater. They bloom on new growth of the season so this does not limit blooming. Deadheading can help encourage blooming. You would remove the inflorescenses as they fade. Cut just above a leaf or branch joint, or if there are sideblooms coming along, just above them. Some gardeners will wait for the main flush of blooms to fade and then lightly shear the plant rather than cut them one by one as it can become tedious on a large plant.
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