When can a woman ask for divorce?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

A wife is required to be patient with her husband and to treat him kindly, since this is on obligation on her.

The Prophet said: “If a woman performs the five daily prayers, fasts, the month of Ramadan, keeps her chastity and obeys her husband, it will be said to her: enter Paradise through any of its gates you wish.” [Ahmad from 'Abdur-Rahmaan Ibn 'Awf]

The Prophet also said: “If I were to command anyone to prostrate to anyone else (other than Allah), I would have commanded the wife to prostrate to her husband.” [At-Tirmithi]

So, a wife is not allowed to ask her husband to divorce her without a genuine reason such as impotency, ill-treatment, etc... In fact, she is required to honor the strong bond of marriage since the Prophet said: “A woman who asks her husband to divorce her without an Islamic sound reason, the smell of Paradise will be forbidden for her.” [Abu Daawood, Ibn Maajah, At-Trimithi, An-Nasaa’i, on the authority of Thawbaan]

But, if she finds no way to gain the love of her husband and in turn to love him, and she fears violating Allah's Orders towards him, then she can seek Khul' (i.e. divorce in return for monetary compensation to be paid by the wife to the husband).

Imam Ibn Qudamah said: “By and large, if a woman hates her husband due to some defect in his character, religion or body, and she fears neglecting his rights on her, then she is allowed to seek Khul'.”

Allah Says (what means): {But if you fear that they will not keep [within] the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself.} [Quran 2: 229]

In the same vein, the wife of Thaabit Ibn Qays came to the Prophet and asked him: “O Allah's Messenger! I do not carp at Thabit concerning his religion or morals, but I fear dishonoring his rights' upon me. Thereupon, the Prophet said: “Will you give him back his garden (i.e. which was given as her bride’s gift)?” She replied: ‘Yes’; and she returned it back to him. Then the Prophet ordered Thaabit to divorce her.” [Al-Bukhari]

Allah knows best.