Her husband left her for a long time with her agreement; is she sinning by not asking for a divorce?
Question

                The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Any woman who asks her husband for a divorce with no reason, the fragrance of Paradise will be forbidden to her.”

 My question: What is the ruling on a wife whose husband left her 4 years ago and she is neither divorced nor is she a wife in any real sense, but she does not want a divorce because she loves him very much, and she hopes that Allaah will guide him and she can go back to him – is she sinning with regard to herself or her husband?.
Praise be to Allah.
    Firstly:  

    Islam has given men a great deal of responsibility, which is 
    to take care of the family and to be the protector and maintainer. The man’s 
    role in fulfilling his duties towards his family is very great, and this 
    role requires him to be present all the time so that he can keep an eye on 
    everything, correct mistakes and guide his young children. He is the 
    mainstay, protector and foundation of this family.  

    If a man neglects his role, that results in unjust treatment 
    for his wife. Allaah says in a hadeeth qudsi: “O My slaves, I have forbidden 
    injustice to Myself and I have made it haraam amongst you, so do not treat 
    one another unjustly.” This may lead to destruction of the family and a 
    great deal of evil may result from this separation, for both the man and the 
    woman. Each of them may take a lover to make up for missing their spouse, 
    for the Shaytaan exploits weak points and flows through the son of Adam like 
    blood. 

    In addition to that, think of the injustice that happens to 
    the children as a result and the shortcoming in taking care of them that 
    means that the woman has to work harder and play the role of both father and 
    mother at the same time. This is something that cannot be done in most 
    cases. We all know the status of the father and the role that he plays in 
    the family, and what may happen when he is not there. How will the children 
    be raised, and how much will they suffer when their father is absent from 
    them? This is what makes children hate their fathers, because they abandoned 
    them and did not take care of them or look after them as they should.  

    Secondly: 

    A man may dislike his wife and not be able to stand being 
    with her any longer. In that case it is prescribed in sharee’ah for him 
    either to keep her in a proper and decent manner or to let her go in a kind 
    manner. He may not be able to keep her in a decent manner because of his 
    intense dislike for her – for example – or for some other reason, so there 
    remains no choice but to be frank, in a kind manner, and divorce her kindly, 
    and give her all her rights in full. 

    The woman may want to stay with him as a wife, so she may ask 
    him to keep her and forego some of her rights over him, such as the division 
    of his time (in the case of a plural marriage) and spending. In that case 
    the man should agree to her request, because that will make her feel good 
    and will mean that he is still being kind to her, especially if that will 
    not cause him any harm or problems. 

    The following verse was revealed concerning such situations 
    (interpretation of the meaning): 
“And if a woman fears 
    cruelty or desertion on her husband’s part, there is no sin on them both if 
    they make terms of peace between themselves; and making peace is better. And 
    human inner-selves are swayed by greed. But if you do good and keep away 
    from evil, verily, Allaah is Ever Well‑Acquainted with what you do”

    [al-Nisa’ 4:128]

    ‘Aa’ishah (may Allaah be pleased with her) said – as narrated 
    by al-Bukhaari (4910) and Muslim (3021) – that this verse was revealed 
    concerning such situations. She said: “ ‘And if a woman fears cruelty or 
    desertion on her husband’s part’ this refers to a woman who is married 
    to a man who does not want to keep her any longer and wants to divorce her 
    and marry someone else, and she says to him: ‘Keep me and do not divorce me, 
    but marry someone else too, and you do not have to spend on me or give me a 
    share of your time.’ This is what Allaah says: ‘there is no sin on them 
    both if they make terms of peace between themselves; and making peace is 
    better’.” 

    Conclusion: 

    It is not permissible for a man to leave his wife for so 
    long; if he does that, then the woman has the right to refer the matter to 
    the qaadi and ask for a divorce so as to avoid harmful consequences. 

    If she chooses to be patient in the hope that Allaah will 
    guide him and he will give up this mistreatment, there is no sin on her in 
    sha Allaah, subject to the condition that this does not expose her to 
    temptation because of her being away from her husband. 

    We ask Allaah to set the affairs of the Muslims straight and 
    to guide them aright. And Allaah knows best.