He promised Allaah that he would give up the secret habit then he did it again. What does he have to do?

We have already explained in the answer to question no.
329
that the secret habit is haraam and how to rid oneself of this habit. The
Muslim does not have to make promises and vows in order to give up the
things that Allaah has forbidden to him. It is sufficient for him to know
that it is haraam and that should be enough to make him give it up. If he
makes a promise or a vow to Allaah not to do the haraam thing then he goes
and does it again, then he has committed the sin of doing something haraam
as well as the sin of breaking a promise or going back on an oath or vow. 

Allaah has enjoined fulfilling promises, as He says
(interpretation of the meaning): 

“And fulfil (every) covenant. Verily, the covenant will
be questioned about”

[al-Isra’ 17:34]

al-Jassaas said: 

The words “and fulfil (every) covenant” mean – and Allaah
knows best – that it is obligatory to fulfil the promises that one makes to
Allaah through vows and promises to do acts of worship. Allaah has obliged
us to fulfil them, as He says (interpretation of the meaning): 

“And of them are some who
made a covenant with Allaah (saying): ‘If He bestowed on us of His Bounty,
we will verily, give Sadaqah (Zakaah and voluntary charity in Allaah’s
Cause) and will be certainly among those who are righteous.’

76. Then when He gave them of His Bounty, they became
niggardly [refused to pay the Sadaqah (Zakaah or voluntary charity)], and
turned away, averse.

77. So He punished them by putting hypocrisy into their
hearts”

[al-Tawbah 9:75-77]

Ahkaam al-Qur’aan, 3/299 

Al-Sarkhasi said: 

Fulfilling promises is obligatory. Allaah says
(interpretation of the meaning): 

“And fulfil the Covenant of Allaah (Bay‘ah: pledge for
Islam) when you have covenanted”

[al-Nahl 16:91]

And He condemns those who do not do fulfil their promises by
saying (interpretation of the meaning): 

“And of them are some who made a covenant with Allaah…”
[al-Tawbah 9:75]. 

Al-Mabsoot, 3/94 

Whoever makes a promise to Allaah to do something and does
not do it, or makes a promise not to do something and does it, then he has
committed the sin of breaking that promise, and he has to offer expiation
for breaking an oath (kafaarat yameen), because a promise is a kind of oath
or vow, and the one who breaks an oath or vow has to offer kafaarat yameen.
He is given the choice of freeing a slave, or feeding ten poor persons, or
clothing them. Whoever cannot do any of these things has to fast for three
days. 

Ibn Qudaamah said: 

If a person says: I solemnly promise to Allaah that I will do
such and such, then this is an oath in which the intention was to swear an
oath to Allaah. 

Al-Mughni, 9/400. 

Shaykh al-Islam Ibn Taymiyah said: 

Promises and vows are verily similar. If a person says: I
promise Allaah that I will do Hajj this year, then this is a vow and a
promise and an oath. If he says, I will not speak to Zayd, this is an oath
and a promise but not a vow. But an oath is a vow when a person promises to
an act or worship or an action by means of which he may draw closer to
Allaah.   

Al-Fataawa al-Kubra, 5/553. 

This is also the view of Ibn ‘Abbaas, Maalik, ‘Ata’,
al-Zuhri, al-Nakha’i, al-Shu’bi and Yahya ibn Sa’eed, as it says in
al-Mudawwanah, 1/579, 580. 

In conclusion: You have to offer kafaarat yameen for breaking
your promise to Allaah. We ask Allaah to bless you with guidance, piety,
chastity and independence of means. 

And Allaah knows best.