Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- I`tikaf is a recommendable act that brings one closer to Allah. It can be practiced any time throughout the year but it is strongly desirable in Ramadan, especially during the last 10 days of this blessed month.
2- If a woman has no choice but to discontinue i`tikaf in Ramadan because of her menses, there is no need for her to make up for it.
Answering your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
I`tikaf is of two types: 1. Mandatory. 2. Recommended.
1- I`tikaf is mandatory on those who have made a vow to Allah to that effect: For instance, if someone says, if I am cured, I will sit in i`tikaf; or if I pass the exam, I will sit in i’tikaf. Once we make a vow we ought to fulfill it. Allah says, “ O you who have believed, fulfill [all] contracts” (Al-Ma’idah 5:1), “And fulfil their vows.” (Al-Hajj 22:29). And the Prophet (peace be upon him) said, “Whoever promises to Allah to do a pious deed, he should fulfill the same.” (Al-Bukhari)
If you happened to break or discontinue an obligatory i`tikaf, you should make up for it later.
2- I`tikaf otherwise is only recommended. It is a supererogatory act entailing rewards. One may choose to sit in i`tikaf any time in a mosque where Jumu`ah is held. However, it is a great Sunnah in the last ten days of Ramadan. The Prophet (peace be upon him) consistently practiced it, and after his death, his wives continued the great tradition.
Since the last type of i`tikaf is not obligatory but a sunnah, if you had no choice but to discontinue, there is no need for you to make up for it. However, you should rest assured, Allah, being infinitely Merciful, will reward you for your intention.
Allah Almighty knows best.