Miss Hazel, the protagonist in "My Man Bovanne," certainly does show independence of spirit and it certainly does keep her from slowing down. This is illustrated particularly well in her reaction to her children's humiliating treatment of her in the kitchen at the party, which was precipitated by her dance with old and blind Bovanne who got into his "hummin jones" and expressed his sightless dance in a way not dependent upon the dance vogue of the day--which he couldn't see. Hazel was saddened and disheartened at her children's cruel assessment of her but she insisted in her heart that though severely (and wholly inappropriately) chastised by her children, who are meant to love and respect her, she still didn't feel ashamed. Had she not had an independent spirit, she would have succumbed to their wrong-headed perspective and felt ashamed of her behavior but as it was, she kept going on doing what she knew was good and right.
Similarly, if she weren't independent, Hazel would have capitulated to their demands that she talk to the Reverend about using the church basement for a "council of elders," thus putting her in a position of obligation to a man she believed to be a hypocrite--as it was, she defied their insistent pressure and refused to speak to the Reverend of their behalf, thereby refusing to slow down in her commitment to sincerity.
Her independence is also particularly well demonstrated when she takes Bovenne home to give him a good bath and good food and have him as a guest at the dinner her children have called for the next night to facilitate a "family conference" night. Hazel's independence in this last situation can be variously interpreted as a straightforward act of generosity and advancing the lot of the elderly in the neighborhood--meaning her independence gave new ways to act instead of slowing down--or as another act of defiance toward her children's unseeing points of view or as a perhaps not so subtle reminder that respecting the elders doesn't start with forcing the establishment of a council of elders but with being kind, loving, accepting and respectful to one neighborhood elderly old blind man. Thus it seems that Hazel's independence is a key factor in a life that does never seem to slow down.