She hates her husband and fears that she may fall into zina if she stays with him

Firstly: 

Zina is a grave sin,
especially on the part of one whom Allaah has blessed with marriage and who
has responded to the blessing with ingratitude, betrayed her husband,
transgressed against his honour and contaminated his bed. Hence the
punishment for this married woman is to be stoned to death, as a punishment
from Allaah, and Allaah is Almighty and All-Wise. 

But by His mercy, He is
kind to His slave and gives him respite and allows him to repent, and He
accepts that from him and gives reward for that. How merciful, great and
kind He is, may He be glorified and exalted. 

Allaah says (interpretation
of the meaning): 

“And those who invoke not any other ilaah (god) along with
Allaah, nor kill such person as Allaah has forbidden, except for just cause,
nor commit illegal sexual intercourse __and whoever does this shall receive the punishment.

69. The torment will be doubled to him on the Day of
Resurrection, and he will abide therein in disgrace;

70. Except those who repent and believe (in Islamic
Monotheism), and do righteous deeds; for those, Allaah will change their
sins into good deeds, and Allaah is Oft‑Forgiving, Most Merciful”

[al-Furqaan 25:68-70]

So continue to repent and
beseech Allaah to accept it from you, and beware of your self that is
inclined towards evil, lest you take for granted Allaah’s kindness towards
you and His covering of your sins, for He gives respite but does not forget,
and when He becomes angry He punishes. 

Secondly: 

You have to block all the
ways that lead to haraam, such as tabarruj (wanton display of adornment),
free mixing, correspondence and phone calls. This is part of your repentance
and mending your ways. You must beware of the traps of the shaytaan, for the
shaytaan has traps and tricks whereby he tempts his friends, as Allaah says
(interpretation of the meaning): 

“O you who believe!
Follow not the footsteps of Shaytaan (Satan). And whosoever follows the
footsteps of Shaytaan (Satan), then, verily, he commands Al‑Fahsha’ [i.e. to
commit indecency (illegal sexual intercourse)], and Al‑Munkar [disbelief and
polytheism (i.e. to do evil and wicked deeds; and to speak or to do what is
forbidden in Islam)]. And had it not been for the Grace of Allaah and His
Mercy on you, not one of you would ever have been pure from sins. But Allaah
purifies (guides to Islam) whom He wills, and Allaah is All‑Hearer,
All‑Knower”

[al-Noor 24:21]

Thirdly: 

If you do not want to stay
with him and you cannot stand him, and you fear that if you do that you will
fall into zina, then there is nothing wrong with you asking for a divorce,
but you should think about the consequences of doing that and what your
situation will be after that. Pray to Allaah for guidance (istikhaarah)
before doing that. See question no.
11981 for information about
the istikhaarah prayer.  

The evidence that it is
permissible to seek a divorce if a woman hates her husband and cannot bear
to stay with him is the report narrated by al-Bukhaari in his Saheeh
(4867), that the wife of Thaabit ibn Qays came to the Prophet (peace
and blessings of Allaah be upon him) and said: “O Messenger of Allaah, I do
not blame Thaabit ibn Qays for any defect in his character or his religious
commitment, but I would hate to commit an act of kufr when I am a Muslim.” 
[Ibn Majaah (2056 added): and I cannot stand him ] The Messenger of Allaah
(peace and blessings of Allaah be upon him) said, “Will you give him back
his garden [which he had given as mahr]?” She said, “Yes.” The Messenger of
Allaah (peace and blessings of Allaah be upon him) said (to Thaabit),
“Accept the garden, and divorce her once.”  

What is meant by “I would
hate to commit an act of kufr when I am Muslim” is: I would hate to do a
deed that is contrary to Islam such as hating my husband or disobeying him
or not fulfilling his rights, and so on. 

See: Fath al-Baari
(9/400). 

But we advise you, before
you ask for a divorce, to try to set things straight first, for divorce is
something that Allaah hates and does not love. So try to appoint a wise man
from your family to speak to your husband and find out the reasons for the
problem, and try to reconcile between you. What you say about his being weak
can be worked out with your husband frankly, for Allaah is not too shy to
tell the truth. If it is the matter of sickness, there is nothing wrong with
him going to the doctor. 

But if it too difficult for
you and your attempts at reconciliation do not succeed, then in sha Allaah
there is nothing wrong with you asking for a divorce in that case. 

We ask Allaah to set our
affairs and those of all the Muslims straight. 

And Allaah knows best.