If One Forgets
The Bahag (R' Shim'on Kayyara, known by the name of his work "Halachot Gedolot"), writes that one who forgets to count one day of the Omer does not continue counting on the remaining days. The reason for this is that the pasuk dealing with the Sefira (Vayikra 23, 15) says: "…seven weeks shall there be complete". We may infer that the counting must be complete, and that missing even once creates a flaw in the mitzvah, and in such a case one may not continue the counting.
The Tosafot and other Rishonim disagree with the Bahag and are of the opinion that even if one forgets a day – or several days – he may continue the Sefira with a bracha (blessing). They feel that logically it does not seem that the whole Sefira constitutes only one mitzvah (since we say the bracha anew every day!) – but rather each day is a mitzvah in itself. Therefore, even someone who has missed counting the Omer on several days – may continue to do so with a bracha.
Many people mistakenly believe that if they forget one day – they have "lost" the mitzvah, and do not continue the Sefira – but this is not true! The Shulchan Aruch ((תפ"ט, ח' rules:
"If one forgets to say the bracha on one of the days – regardless of whether it is the first day or any other – he should count the remaining days without a bracha."
One must continue the Sefira – albeit with no bracha, because - according to most Rishonim – each day is a mitzvah in itself. On the issue of the bracha – since we are able to fulfill the mitzvah even with no bracha, and we wish to avoid the problem of "bracha l'vatala" (making a bracha in vain), our Rabbis ruled stringently not to say the bracha (in accordance with the Bahag's opinion). However, as far as the basic halacha is concerned – the obligation to continue counting remains, as if one never forgot to count at all. In Case of Doubt:
What should one do if he is not sure whether he missed a day of the Sefira or not? R' Israel Isserlein, in his Responsa "Terumat HaDeshen" rules that in such a case one may continue to count with a bracha. The Shulchan Aruch (ibid.) is also of this opinion. Why? The Pri Chadash (R' Hezekiah da Silva) on the Shulchan Aruch there explains that this is an example of a "sfeik sfeika" – a double (or multiple) doubt. This is a halachic principle meaning that in a case in which combines several (at least two) sfeikot (doubts) – we rule leniently, despite the fact that in the case of each individual doubt – we would rule stringently! Our case combines two doubts:
A doubt pertaining to the reality – since we are not sure that in fact the person did not count the Omer.
A doubt pertaining to the halachic ruling – since even if the person did indeed forget to count, the opinion of most of the Rishonim is that he may continue to say the bracha (even though we do not generally rule this way).
The combination of the two separate sfeikot leads to the conclusion that it is permitted to continue counting with a bracha (and the Mishna Berurah brings this halacha there).
R' Avraham Shmuel Binyamin Sofer, in "K'tav Sofer", explains this halacha differently. In his opinion, in principle we rule in accordance to the Tosafot, that even if one missed a day of Sefira he continues to count. It is only because of "ספק ברכות להקל" ("when in doubt on issues of berachot – we rule leniently") that he does not continue saying the bracha (since it is possible to fulfill the mitzvah even without a bracha).Therefore, one more slight doubt is enough to allow counting with a bracha. Summary
Even someone who forgets to count the Omer on one (or several) days – has not "lost" the mitzvah. He must continue to count meticulously, as according to most Rishonim he is still fulfilling the mitzvah. As a matter of fact, missing Sefira once obligates him to make an extra effort not to forget again! However, he counts without a bracha, thus taking the Bahag's opinion (that he has lost the mitzvah and so should not make a bracha in vain) into consideration. (In case he forgot to count at night, but remembered during the next day – he counts without a bracha when he remembers, and goes back to counting with a bracha the next night). In any case, one who is counting without a bracha should have a clear intention to make the cantor his "agent" for the bracha, or ask someone else to say the bracha as his agent. He should answer "Amen" after the bracha – thus "gaining" the bracha too. (Mishna Berurah, סעיף קטן ל"ז)
 Brought by the Tosafot on Menachot p. 66A, s.v. "."זכר
 סימן ל"ז
 סעיף קטן ל"ח
 On Yoreh De'ah, part 2 the end of .סימן קפ"א