[Re]counting the Omer

One might think that] If one forgets and doesn't count an entire day, subsequently, one may not count for there would not be   . Rather, the Torah only said    [to teach] that the counting begins at night and not that they [the
days] should exclude one another; for every day is a mitzvah in and of itself...From the fact that we make a (separate) blessing every night, learn from this that each and every day is a mitzvah in and of itself and one does not prevent another. (Rabbi Isaiah ben Mali Di Trani (1180-1250, Italy) Sefer ha-Makriah, Sof Halakha 29)

The BeHaG also wrote that if one forgets to make a blessing one of the days,
then a blessing should not be said subsequently. Rav Sa'adia wrote that if one
forgets an entire day, a blessing may be recited subsequently, with the exception of the first night. If one forgets (the first night) and doesn't say a blessing, a blessing may not be said any longer. And Rav Hai wrote that whether it is the first night or any other, if one forgot to make a blessing on it, a blessing may (still) be made on the remaining nights. And Rabbeinu Yonah also wrote this. ((Rabbi Ya'acov ben Asher, Arba'ah Turim, O. H. 489:8)

The Ran wrote at the end of Chapter Arvei Pesahim in the name of Mar Yehudai, that the one who doesn't count the Omer on the first night, counting may not be done subsequently. [Explanation: because   tmimot is required, but the rest of the nights] if one doesn't count at night, counting may be done during the day. And Rav Hai disagrees and says, "That if it is because tmimot   is needed, if one forgot one of the other nights [not the first] the requisite 49 would still not be fulfilled! Therefore, Rav Hai says that if one doesn't count at night, [one may] count during the day (even for the first night)." [End of Rav Hai.] And this teaches us that Rav Hai is also only dealing with the one who forgets at night and remembers the next day, but where one doesn't remember the next day, it is possible that he [Rav Hai] reasons that making a blessing may not continue at all. However, our Rabbi [the Tur] writes that the opinion of Rabbeinu Hai is like Rabbeinu Yonah, since he [Rabbeinu Yonah] reasons that each and every night is a mitzvah in-and-of itself, so surely if one doesn't remember the next day, making a blessing on subsequent nights may continue. (Beit Yosef, O.H. 489:8)

Rav Saadia wrote that if one forgets an entire day, a blessing may be recited
subsequently, with the exception of the first night. If one forgets (the first night) and doesn't say a blessing, a blessing may not be said any longer. (Tur, ibid)

Rav Saadia Gaon reasons that the entire Sefirat ha-Omer is one mitzvah. It begins on the 16th of Nissan and concludes on the 5th of Sivan. Therefore, when one begins to count on the 1st night, the mitzvah has begin, and even though a subsequent night is forgotten, there is nothing to that! [i.e. it has no halakhic significance] And one continues to make blessing on subsequent nights, for one is only continuing the mitzvah that has already been started. However, if one forgets the first night one may not begin to count anymore for the mitzvah of counting does not begin on the 17th of Nissan or any other day. Because the time to begin the mitzvah has passed, it is nullified completely. (R. Joel Sirkes, BaH, O.H. 489:8)

"One counts without a blessing" (D"H from the Kitzer S"A): This is the opinion of the Shulhan Arukh and the Ahronim. [But] see in Sefer Otzar Ha-Hayyim (R. Yitzhak Safrin from Karmona, 1806 - 1874) who brings [the opinion] that if one forgets to count [a 24-hour period] counting may continue with a blessing since the majority of Rishonim interpreted each and every day to be a mitzvah in-and-of itself. And he [Otzar Ha-Hayyim] also brought that all the rebbes that were students of the Besht followed this practice [end quote Otzar Ha-Hayyim]. And I [Rabbi Braun] heard that the reason they followed this custom [of continuing with a blessing] against the Shulhan Arukh is because earlier times are not like later ones (i.e., the time of R. Karo is different from our time). Earlier, people were meticulous about counting the Omer and if they forgot to count once, they still counted but without a blessing, since blessings don't prevent one from fulfilling the obligation. But in our time [strict] religious Judaism is declining rapidly and if we tell someone to keep counting without a blessing, [this person] will think that they aren't actually fulfilling any obligation and won't be scrupulous to continue counting [at all]! Therefore, instruct those who come and ask [what to do if they miss a day] that they should count with a blessing, since in any event this was the opinion of the Rishonim. (R. Shlomo Zalman Braun Shearim Metzuyanim Be-Halakhah (120:4).)

From the perspective of positive historical Judaism, Jewish practice is a developing organism, which moves organically rather than linearly. Jewish law rarely speaks only in one voice, and often evinces a range of responses that reflects the life of the Jewish people in different ages and locations. A healthy respect for halakhic pluralism encourages reclaiming a more flexible alternative to the stringency of prohibiting recital of a berakhah after a 24-hour lapse.

A second consideration emerges from the nature of how our people grow in observance. Judaism, while affirming the obligatory nature of halakhah as a whole, has encouraged a pedagogy of gradual growth and a resistance to the kind of all-or-nothing mentality that would preclude most of our people from exploring the possibility of a deeper engagement with halakhah and mitzvot.     Tafasta merubeh lo tafasta, excessive stringency may discourage growth in
mitzvah observance. We must help cultivate an atmosphere of increasing observance by celebrating each positive step forward, rather than necessarily imposing a stultifying all-or-nothing approach to observance. To encourage our people to grow gradually in mitzvot in a host of areas is a prudent pedagogical response both to the living nature of Torah and to creating access for our people to meaningful growth in shmirat mitzvot.
In light of the encouragement Judaism offers to exploring greater observance and our recognition that many Jews can only reclaim their heritage if encouraged to move from where they are gradually, it is counter-intuitive and counter-productive to always assert a rigid line separating those who observe the mitzvah each and every day from those who might occasionally forget. As we seek to help Jews maximize their observance, maintaining a rule which discourages engagement in the mitzvah seems misguided and out of character.
At the same time, this return to permit an earlier position is rooted in education and a pedagogy of encouragement and gradualism, rather than in an ethical imperative. As such, there is no need to prohibit the form in which most Jews have observed sefirat ha-omer since the time of the Shulhan Arukh. Jews who observe this mitzvah ought to be able to rely on the historical consensus of generations of faithful Jews, and we are not interested in calling that commitment into question. (Brad Artsen & Aaron Alexander, A Missed Day in the Life of the Omer)