The day of doubt is the 30th day of Sha`ban. It is given that name because there is a doubt regarding the number of days of the month of Sha`ban; they may be 30 or 29. There are also some texts forbidding fasting the one or two days preceding Ramadan. In the hadith, "Do not precede the month of Ramadan with one or two days of fasting, unless it is the habit of any of you (i.e., the person is not specifying these days but ordinarily fasts on them and the few days before them)."
Most of the scholars deemed it reprehensible to precede the fasting of Ramadan with fasting the last one or two days of Sha`ban. Also, fasting the day of doubt is an act of disobedience, for the Prophet (peace and blessings be upon him) said: "Whoever fasts the day of doubt, has disobeyed Abul-Qasim (i.e. The Prophet)." This is the view of Malik, Ahmad, Ash-Shafi`i and others.
Most of the scholars hold the view that if a person fasts on that day and then it shows up that the day is one of the days of Ramadan, he has to make up for it. The simple reason for this is that by fasting that day, he does not make intention to fast the day of Ramadan, and the lack of the intention leads to the invalidity of the fast on that day. In fact, when a person fasts that day he cannot ascertain whether it is a day of Ramadan or not since it is a day of doubt. Intention is to be based on certainty.
If it is his habit to fast Mondays, for example, and this day happens to be Monday, then it is okay since he is certain of his intention. Thus, the day will be counted as nafl (voluntary) fasting if it shows up to be the 30th of Sha`ban, and it will be considered fard (obligatory) if it shows up to be the first of Ramadan. This is the view of Hanafis.
Some Companions agree that it is allowable to fast on the day of doubt. Among those Companions are `A’ishah, `Umar, Ibn `Umar, Anas ibn Malik, Abu Hurayrah, Mu`awiyah and `Amr ibn Al-`Aas (may Allah be pleased with them).
As for the wisdom of not fasting on that day, there are different opinions in this regard. All in all, Ibn Hajar states that such fasting goes in contrary with the ruling that links the beginning of fasting to the sighting of the new moon, which can be deduced from the hadith of the Prophet.
It is clear that if one has to make up for a missed day of the obligatory fasting from the previous Ramadan and has no other chance except that day (i.e., the day of doubt), then he can fast. Also, if someone makes a vow to fast a specific day and it happens to be the day of doubt, then fasting is permitted and he incurs no sin.