Our Gemara on Amud Beis discusses the biblical directive to rebuke a sinner. The verse states (Vayikra 19:16): “הוֹכֵ֤חַ תּוֹכִ֙יחַ֙ אֶת־עֲמִיתֶ֔ךָ You shall admonish, and indeed admonish your fellow country man.”  

Biblical Hebrew has an idiomatic word form where a verb is repeated, presumably to connote emphasis.  The halachic implications of this emphasis are discussed in our Gemara:

Rava said to him: “Hocheach” indicates that one must rebuke another even one hundred times. “Tokhiach” teaches another matter: I have derived only the obligation of a teacher to rebuke a student. With regard to the obligation for a student to rebuke a teacher, from where is it derived? The verse states: “Hocheach Tokhiach” to teach that one is obligated to rebuke another in any case that warrants rebuke.

Word one of admonish teaches an obligation to be persistent. Word two of admonish teaches that one may even go beyond what might be considered protocol.

Despite our Gemara learning that there is emphasis and imperative to admonish, even 100 times, the Gemara elsewhere (Yevamos 65b) teaches a mitigating idea:

Just as it is a mitzvah for a person to say that which will be heeded, so is it a mitzvah for a person not to say that which will not be heeded. One should not rebuke those who will be unreceptive to his message. Rabbi Abba says: It is obligatory for him to refrain from speaking, as it is stated: “Do not reprove a scorner lest he hate you; reprove a wise man and he will love you” (Mishley 9:8)

Rashi (ibid) explains the rationale of the Gemara as derived from the doubling of the word to admonish, thus effectively reading it, as “admonish in a way that is an effective admonition”. 

Rashi’s explanation of the Gemara Yevamos invents a derasha that is not found in our Gemara in Bava Metzia.  The Maharsha in Yevamos seems to be asking this question of Rashi, though indirectly. Yismach Moshe (Devarim 1) elaborates on the question, asserting that it is not merely an additional derasha, but one that is contradictory to the one in Bava Metzia. Our Gemara learns from the first word “admonish”, that there is an imperative to admonish thoroughly, even 100 times.  Thus, the repetition of the word admonish indicates an intensification, to even admonish a teacher.  Yet, in Yevamos, at least the way Rashi would explain it, the second admonish mitigates the imperative, so that one should not admonish a person who won’t listen.  Yismach Moshe also points out a logical problem with Rashi. If we already learn that a person is obligated to rebuke even 100 times, this would imply rebuking a stubborn person who is not listening, which contradicts the Gemara in Yevamos that says we should not rebuke a person who won’t listen. Technically, one could differentiate between a person who is quite stubborn and takes 100 times to break through and convince them versus someone who will never listen, but Yismach Moshe rightfully asserts that is a rather unlikely distinction.

Therefore Yismach Moshe suggests the following answer. The basis for not rebuking someone who will not listen comes from the ruling of Gemara Beitzah (30a), which says that one should not rebuke people who will not listen, as it is better that they be erring due to lack of knowledge instead of intentionally violating.  Thus, Gemara Yevamos, says if you estimate that a person won’t listen, then better not to admonish him in the first place.  On the other hand, if you estimated incorrectly, and gave him admonition, and he did not listen, now you must continue even 100 times because there no longer is a reason to hold back so that he errs instead of acting deliberately. Since he was already rebuked, “the cat is out of the bag”, and he is sinning deliberately. Therefore, there is an obligation to continue to rebuke.  Additionally, our Gemara also learns that one is to even admonish a rebbe, as one might think he would be unlikely to listen to a student. The verse repeats itself to encourage against making that assumption. But that does not contradict the teaching in Yevamos, which says after all, if one truly believes the person won’t listen, it is best not to start up at all.  

We might ask, granted, there is no longer a reason to hold back once the first rebuke began, since there is already a demonstration of knowledge and  nonetheless a will to sin, but why should one keep rebuking?  What is the function of a continuous rebuke if the person clearly is not listening?  One might answer, since there is no downside, we should hope against hope, that somehow the rebukes will eventually penetrate. Or, we can say that even if the person will not listen, it is good for the bystanders and even the observer to object. This is either to maintain personal standards or to simply defend the honor of the Torah. (Rav Soloveitchik develops this idea differently, see Reshimas Shiurim on our Gemara.)