Before I went to bed, I made the intention to fast a day that I missed in Ramadan. The following day, I almost forgot I was fasting as I ate and drank normally. Moreover, my husband had sexual intercourse with me. About one hour before Maghrib, I remembered. So I abstained from whatever breaks fasting until the Maghrib. Is my fast valid?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

The fasting of the days that one misses in Ramadan is obligatory, and therefore such fasting requires one to make the intention for it the night before the day of fasting. The Prophet, sallallaahu ‘alayhi wa sallam, says, “If a person did not make the intention for fasting at night before the day he would be fasting, then his fasting would not count.” [An-Nasa’i] Since you had made the intention for fasting the night before your fasting day, then the fasting should be valid. That you have forgetfully done things that invalidate fasting should have no effect on the validity of your fast. Excluding Maalik, the predominant view is that whoever forgetfully eats or drinks while fasting, his fasting remains valid. It does not matter how much you ate or drank as long as you did not deliberately intend to do any of these things that invalidate fasting (with the intention of braking your fast).

An-Nawawi says:

If a fasting person forgetfully eats, drinks, throws up, takes a medicine, has sexual intercourse, or does any of the other things that invalidate fasting, then his fasting shall remain valid, no matter how much he has done of these things. This is the opinion of the school, its founder, the majority the scholars of Iraq, and others.

The prominent opinion of the Hanbali school is that if a fasting person forgetfully has sexual intercourse, then his fasting becomes invalid and he must make up for the day later, in addition to observing the expiation that is prescribed for this. The sound opinion, however, is view of the majority, which states that having sexual intercourse out of forgetfulness does not invalidate one’s fast.

In Ar-RawdhAl-Murbi‘ and its commentary, Ibn Qasim says:

If a fasting person has sexual intercourse during the daytime in Ramadan, even if forgetfully, ignorantly, or by being forced to do so, he is required to make up for the day of fasting later, in addition to observing the expiation that is prescribed in this regard. It does not matter whether or not he ejaculated. This is because the Prophet, sallallaahu ‘alayhi wa sallam, did not provide such details.

He has also been quoted maintaining that the fasting person in hand is required to neither make up for the day nor observe the expiation. This is the view of Abu Haneefah and Ash-Shafi‘i. An-Nawawi says that this is the majority view of the Muslim scholars and the soundest of their opinions in this connection. This is because the Hadith categorically states that whoever forgetfully eats while fasting, his fasting should remain valid. Sexual intercourse should be treated the same in this regard. The Hadeeths that state otherwise pertain to the one who deliberately breaks his fast. During the lifetime of the Prophet, sallallaahu ‘alayhi wa sallam, a fasting person had sexual intercourse with his wife. He came to the Prophet, sallallaahu ‘alayhi wa sallam, and said, “O Prophet! I ruined myself.” The Hadeeth obviously indicates that the man deliberately broke his fast since there should be no guilt on the part of the one who forgetfully breaks his fast.

That being said, your fasting is valid, and you are not required to repeat the day. If you would like to fast a day in place of the day in question just for the sake of assurance, then that should be fine. There is no expiation on you either since the day you mentioned was not in Ramadan. Therefore, there is no expiation for breaking your fast, even if deliberately, outside Ramadan. 

Ibn Rushd says, “The majority of the Muslim scholars agree that deliberately breaking a fast that one missed in Ramadan does not entail expiation because such fasting occurs outside Ramadan and, therefore, the event does not have the same sacredness as that of Ramadan."

Allah knows best.