Unfortunately we can't determine what the cause is since there are no indications of a particular pest, disease, or environmental issue in the photo. A secondary infection (one that takes advantage of pre-existing plant stress like drought, even if not manifesting symptoms yet) like Botryosphaeria canker is possible, but we can't confirm it from the photo. Fothergilla is in the witchhazel plant family, though we don't think this is necessarily one of the common fungal ailments that witchhazel gets (Phyllosticta leaf blotch). A stem-boring insect (also generally targeting stressed plants) could be responsible, like beetles, but unless you split open the dying stem near the base, you might not be able to detect them. Usually, though, advanced damage to the inner wood results in visible bark cracking, sap oozing, and/or sawdust residue being pushed out of the borer's tunnel.

Regardless of the cause, it doesn't look like that branch will recover, so we recommend that it be pruned off. New growth should fill that gap in over time, assuming the issue doesn't spread. No pesticide treatment is warranted, nor would fertilizer be helpful, so other than pruning and continuing to monitor the plant for watering needs, no action needs to be taken at present.

Miri