Should she seek separation from her husband because he does the secret habit?

There is no doubt that the husband’s having intercourse with his wife and giving her her rights to sexual fulfilment and satisfying her desires, according to what he is able to do and what is appropriate in his circumstances, is one of the greatest rights that the wife has over her husband, and it is one of the most important implications of living with them honourably. Allah, may He be exalted, says (interpretation of the meaning):

“And live with them honourably”

[an-Nisa 4:19].

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:

It is obligatory for the man to have intercourse with his wife on a reasonable basis, and this is one of the most important rights that she has over him; it is more important than feeding her. With regard to what is obligatory in terms of intercourse, it was said that what is required is once every four months, or it was said that it is according to her need and his ability, just as he should feed her according to her need and what he can afford. This is the more correct of the two scholarly opinions.

End quote from Majmoo‘ al-Fatawa, 32/271

Based on that, this serious problem should be solved. What this husband is doing, in addition to its being disobedience towards Allah, may He be glorified and exalted, in and of itself, even if it did not result in affecting the wife’s rights, and even if he was not married in the first place, one of the most serious effects of what the wife has mentioned here is that it leads to neglect of the wife’s right to kind and honourable treatment, and it is satisfying his desire outside of the vessel prescribed in sharee‘ah, and neglecting the vessel prescribed in sharee‘ah and leaving its needs unmet. This is one of the gravest kinds of neglect and foolishness, and it is a deviation from the aims of sharee‘ah.

But first of all you should start by advising your husband and trying to come to some understanding with him concerning that; explain to him that this is haram according to the religion of Allah, and that it is haram to neglect the rights of the wife or to be heedless concerning them.

If advice turns out to be to no avail, and this act of his results in what you have mentioned of depriving you of your shar‘i rights and exposing you to temptation, then you have the right to ask for khul‘ or divorce (talaq) from him.

Shaykh al-Islam [Ibn Taymiyah] said:

If the wife is adversely affected by the husband’s failing to have intercourse with her, this permits annulment of the marriage in all cases, whether the husband did that deliberately or not, or whether he was able to have intercourse or not. This is like the ruling on maintenance (if the husband fails to spend on his wife’s maintenance), and is even more important.

End quote from al-Fatawa al-Kubra, 5/481-482