The Shulchan Arukh (O.C. 673:2) codifies the well-known halakha of “kaveta ein zakuk lah,” which means that if one’s Chanukah candle was extinguished after it was lit, he is not required to rekindle it. Even though the candle did not burn for the minimum required duration, nevertheless, as long as it was lit with enough oil to burn for this period and under the proper conditions, one has fulfilled the mitzva and does not have to light the candle again. This issue is subject to a debate among the Amoraim (Shabbat 21a-b), and Halakha follows the position that one does not have to light a Chanukah candle that was extinguished after having been properly lit.
However, numerous Acharonim, including the Peri Megadim (Eishel Avraham, 673:12), Rav Yaakov Emden (in Mor U-ketzi’a) and the Avnei Neizer (503), qualify this ruling, and maintain that it applies only if the flame was extinguished unintentionally. If, one purposely extinguished the candle, for whatever reason, before it burned for the minimum-required duration, then he is required to rekindle the flame.
An exception is the Sefat Emet, in his commentary to Masekhet Shabbat (21b), who writes that even if one intentionally extinguished the candle, he has fulfilled his obligation and does not need to rekindle the flame. The Sefat Emet draws proof to this position from the Gemara’s discussion of the subject. The Gemara attempts to disprove the opinion of “kaveta ein zakuk lah” based on the berayta’s comment that the obligation of Chanukah candles extends until people are no longer walking about outdoors in the evening. This might be understood to mean that as long as people are walking about, one is required to ensure that his candles are lit, and thus he must rekindle a flame that has been extinguished. The Gemara dismisses this argument, however, explaining that the berayta refers either to the fact that one who did not light at the ideal time is still required to light as long as people are walking about outside, or that one must initially place the amount of oil necessary to sustain the flame as long as people are walking about. The Sefat Emet notes that the Gemara could have refuted this proof differently, by suggesting that the berayta refers to one who intentionally extinguished the candle. If, indeed, the view of kaveta ein zakuk lah concedes that one must rekindle the flame if he extinguished it intentionally, then the beraya can be reconciled with this view if we explain it as requiring rekindling the flame that one had purposely extinguished, as long as people are still walking about. The fact that the Gemara did not suggest this reading of the berayta suggests that this assumption is incorrect, as according to the view of kaveta ein zakuk lah, one does not have to rekindle the flame even if it was extinguished intentionally.
Rav Asher Weiss dismisses this argument, noting that the Gemara did not find it reasonable to explain the berayta in this vain. The Gemara occasionally advances the argument of “atu bi-r’shi’i askinan” (literally, “Are we really dealing with wicked people?”), which means that we do not assume a Mishna or berayta speaks of wicked people, unless this is clearly indicated. It stands to reason that in this instance, too, the Gemara did not accept the possibility that the berayta addresses the case of a person who intentionally extinguished the Chanukah candles.