Her husband only gives her maintenance, and he lives far away from her. Can she ask for a divorce?

Praise be to Allah.

Firstly: 

Allah has permitted a man to have several wives, and has forbidden men to mistreat their wives. If a man wants to have more than one wife, then he can keep the first wife on a decent and reasonable basis, or he can let her go in a kindly manner. It is not permissible for him to keep her married to him whilst forsaking her and not giving her her rights. It is not permissible for him to be negligent with regard to his family and the upbringing of his children. Plural marriage has not been prescribed in order to destroy families, rather it is prescribed to build families and increase their numbers. 

This forsaking of his wife and negligence is haram for him, even if he had another wife according to sharee’ah, so how about if he is forsaking his wife and neglecting his family for an illegitimate reason such as a haram relationship and corrupt desires? 

Secondly: 

The wife has the right to ask for a divorce from her husband if she cannot bear his bad treatment. This does not mean that she does not accept the decree of Allah. Indeed in some cases it may be haram for her to stay with a husband who commits major sins and whose children are not safe from his evil influence and bad treatment. As divorce is allowed in Islam and it may even be obligatory to ask for a divorce in some cases, there is no need to think that this may go against belief in the divine will and decree, because Allah has decreed both marriage and divorce. 

The wife has the right to live with her husband and be treated in a decent and reasonable manner, and to have a husband with whom she can feel happy and who will be like a garment for her, so that there will be love and compassion between them. This is the reason for which marriage was prescribed, and if anything detracts from what we have mentioned, then it is contrary to the reason for which marriage was prescribed. 

Hence the husband should choose a woman who is religiously-committed, and fathers and guardians should marry their daughters and female relatives under their care to men who are religiously-committed and of good character, because if the Muslim household is established on the basis of the laws of Allah, no wrongdoing or cruelty will be seen in it. If a wife dislikes her husband for a legitimate shar’i reason, then she can ask for divorce (talaq) or can divorce him by khul’, and if he dislikes her he can divorce her by talaq and give her her rights in full. He should either retain her on reasonable terms or release her with kindness.  

If divorce takes place, then Allah may decree that she finds a good, righteous husband, as He says (interpretation of the meaning): 

“But if they separate (by divorce), Allah will provide abundance for everyone of them from His Bounty”

[al-Nisa 4:130] 

Thirdly: 

Some women stay and put up with their husbands because of the possibility that Allah may reform them, or so that he will remain in contact with his children and take care of them and spend on them. If a long time goes by and he does not reform or he mistreats his wife and children too much, and she has sufficient money to spend on herself and her children, then there is no point in her staying with him. Rather the right thing to do is to rid herself of him so that she can live a better and more decent life, and raise her children to obey Allah and His Messenger (peace and blessings of Allah be upon him). 

You should take stock of yourself and repent to Allah for any sins or transgressions that you may have committed against the rights of Allah or the rights of your husband, or anyone else. Perhaps what has happened to you may be a punishment for a sin that you have committed, because Allah says (interpretation of the meaning): 

“And whatever of misfortune befalls you, it is because of what your hands have earned. And He pardons much”

[al-Shoora 42:30] 

Think long and hard about your situation and how likely it is that you may find a husband after him or live a peaceful life without him. Consult people around you who are close to you and are sincere. I advise you, if they agree with you, to divorce him if the situation is as you describe in your question. So pray istikharah and ask Allah for guidance, and if you feel at ease with the idea of divorce then go ahead, and ask Allah to make you independent of means by His bounty. We ask Allah to set your affairs straight and to relieve your distress and reconcile between you if that is better for you both. 

And Allah knows best.