While Hurston never really gives a definitive reason as to why Delia stays with Sykes, one potential reason might be her spiritual beliefs.
Hurston associates Delia with Christian notions of the good life. Delia is very pious in how she approaches going to church and following church edicts. In fact, at the point we are introduced to her, going to church and doing her job as a washer woman are really the only two things she enjoys in life. Hurston alludes to this Christian construction with descriptions of Delia's "meekness." She refers to Delia's "stooped shoulders" and the way her "work-worn knees crawled over the earth in Gethsemane and up the rocks of Cavalry many, many times." Such imagery enables the reader to see Delia as a product of spiritual faith.
This might be the reason why she stays with Sykes. She believes that a sense of justice will prevail. Since she is so spiritually driven, Delia could not contemplate divorce because of how it would be seen as a transgression to the sacred institution of marriage. Divorce would also reject the natural order that Delia believes is a part of the universe: "Whatever goes over the Devil’s back, is got to come under his belly. Sometime or ruther, Sykes, like everybody else, is gointer reap his sowing." Delia might have stayed with Sykes for this long, despite his cruelty, because she believes that her faith will be rewarded.
It's also true that Delia loved Sykes at one point. She once had strong feelings for him: ‘‘Ah hates you tuh de same degree dat Ah useter love yuh." Delia might believe that her love will be rewarded. Her faith in goodness extends to the purity of love, something that she once had for Sykes. Just as remaining with him is a testament of her religious faith, staying with him recognizes the love she once had for him.
In conclusion, Delia's faith in divinity and in love might be reasons she stays with him. These strong convictions serve as pillars of her faith and could explain why she would stay with someone like Sykes.