some very practical reasons.

The text tells us that Delia's income has paid for the house the couple lives in.

Mah tub of suds is filled yo' belly with vittles more times than yo' hands is filled it. Mah sweat is done paid for this house and Ah reckon Ah kin keep on sweatin' in it. . . . You aint paid for nothin' on this place, and Ah'm gointer stay right heah till Ah'm toted out foot foremost."

In the passage above, it makes sense that Delia wants to protect her investment. After all, the house is a testament to her life's work. For his part, Sykes shows no gratitude for all that Delia has done. Instead, he treats his wife as if she is no better than a pack mule. Delia also knows that Sykes wants her out of the house for a very selfish reason: he is aiming to move his mistress (Bertha) into the house. Sykes uses ridicule and violence to try to goad Delia into leaving.

When his violent tirades fail, Sykes brings in a rattlesnake, a creature that Delia is deathly afraid of. For her part, Delia decides to dig in her heels because of everything she has put into making a home. Also, the house is more than a temporary abode to her. The text tells us that Delia built it for her "old days." Over the years, she has planted flowers and trees on the property, ones that she knows will gladden her heart in her twilight years.

Seen in this light, Delia's behavior makes a little more sense: she has worked too hard to meekly give up her home to a faithless man and his mistress.

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.