She made a pledge to Allah that she would give up a habit, but she did not fulfil that pledge. What must she do?

Firstly:

Ruling on making a pledge to Allah, may He be exalted, to encourage oneself to do something or stop doing something

If making a pledge to Allah, may He be exalted, is done to encourage yourself to do something or to stop doing something, then it comes under the same ruling as an oath.

Shaykh al-Islam (may Allah have mercy on him) said: If a person says: I pledge to Allah that I shall do Hajj this year, then this is a vow, a pledge and an oath. If he says: I shall not speak to Zayd, it is an oath and a pledge, but it is not a vow.

If an oath includes the meaning of a vow, which is a commitment to Allah to do an act that will bring him closer to Him, then it must be fulfilled." (Al-Mustadrak ‘ala Majmoo‘ al-Fataawa  5/144).

Please see the answer to question no. 187335 .

Secondly

Ruling on one who makes a pledge to Allah to do something, but does not fulfil that

If you made the pledge mentioned to Allah, then you must offer expiation for breaking an oath (kaffaarat yameen), because this was a vow to do something permissible, which is giving up any permissible habit. But there is no obligation to fulfil it; rather the person has the choice between fulfilling it or offering expiation for breaking an oath.

Ibn Qudaamah (may Allah have mercy on him) said: Vows are of seven types…

The fifth type of vow is that which is permissible, such as putting on a garment, riding a mount, or divorcing a woman in a permissible manner. In this case, the one who made the vow has the option of doing it and fulfilling what he vowed to do, because of the report which says that a woman came to the Prophet (blessings and peace of Allah be upon him) and said: I vowed to beat the duff (a type of hand-drum) in front of you. The Messenger of Allah (blessings and peace of Allah be upon him) said: “Fulfil your vow.” Narrated by Abu Dawood.

And because if a person swore he would do a permissible action, he should fulfil it. The same applies if he vows to do it, because a vow is like an oath.

Or if he wishes, he may refrain from doing it, in which case he must offer expiation for breaking an oath…

With regard to the hadith about the woman who vowed to walk, [the Prophet (blessings and peace of Allah be upon him)] enjoined her to offer expiation in another hadith. ‘Uqbah ibn ‘Aamir narrated that his sister vowed to walk to the Sacred House of Allah. The Messenger of Allah (blessings and peace of Allah be upon him) was asked about that, and he said: “Tell her to ride and let her offer expiation for breaking her oath.” Saheeh; narrated by Abu Dawood. This addition must be taken into account." (Al-Mughni  10/70).

The expiation does not have to be repeated if you break the oath again, because there is nothing in the wording to indicate that it should be repeated.

The expiation for breaking an oath is freeing a slave, or feeding ten poor persons, or clothing them. Whoever cannot afford to do that must fast for three days, because Allah, may He be exalted, says (interpretation of the meaning):

{Allah will not impose blame upon you for what is meaningless in your oaths, but He will impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] – then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths} [al-Maa’idah 5:89].

It is acceptable to give each poor person a meal, or one and a half kilograms of rice.

And Allah knows best.