Should one use new wicks each night?
It is permitted to reuse the same wicks of the previous night for the next nights lighting. [Some Poskim, however, write that the custom is to use new wicks each night. There is no final arbitration in this matter, and each is to follow his custom. Some Poskim write that if one decides to use the old wicks, then he should place the old wick of the first candle which was lit the previous night, within the candle which will be lit first tonight. Other Poskim however, write that doing so is not necessary, and so is the custom, not to be particular in this matter.]
The Chabad custom: In Sefer Haminhagim, although both approaches [to reuse same wicks versus new wicks] are recorded, it plainly states that the custom is to use new wicks each night, although concluding that they have not verified the custom of the Rebbe Rayatz. Practically, however, the custom of the Previous Rebbe has been corroborated that he would reuse the same wicks each night. However, it is testified that the people who set up the Rebbe’s Menorah used new wicks each night, however they testify that they did not receive a directive from the Rebbe in this matter and did this on their own initiative. In conclusion, it seems that there is no conclusive Chabad custom in this matter, and whatever approach one chooses has upon whom to rely.
 Michaber 673:4; See Sefer Haminhagim p. 160 [English] in footnotes; Chikrei Minhagim 3:230
 Michaber ibid “We do not worry to switch the wicks, until they have become consumed”; Implication of Tur 677; Miseches Sofrim 20:4; Shibulei Haleket 185; Abudarham Seder Ner Chanukah p. 200 based on Rashi; Peri Chadash 673; Kitzur SHU”A 139:4; Siddur Yaavetz; Custom of Chasam Sofer
The reason: Although using the same old wicks may seem like a belittlement to the Mitzvah, nevertheless, it is permitted to do so being that on the contrary, such wicks are easier to light. [Levush 673; M”B 673:31; Kaf Hachaim 673:71] Alternatively, it is proper to do a second Mitzvah with an item which was already used for a Mitzvah. [Toras Menachem 15:303, printed in Shulchan Menachem 3:271] Alternatively, as the laws of the Chnuakh candles do not follow the exact same laws as the Temple Menorah lighting. [Shulchan Gavoa 673:4]
 Darkei Moshe 673:6 in name of Kol Bo 44; Abudarham ibid that so is custom [even though he personally negates]; Tanya Rabasi Hadlakas Neiros 35; Orchos Chaim Chanukah 5; Meiri Shabbos 21b; Ohel Moed 2:2; Leket Yosher p. 152 that so was custom of Terumos Hadeshen; Seder Hayom Chanukah p. 236; Elya Raba 673:16; Shulchan Gavoa 673:14; Mishmeres Shalom 48:3 that so was custom of his forefathers; Custom of Darkei Teshuvah and Munkatcher Rebbe; Kaf Hachaim 673:72; Sefer Haminhagim p. 160 [English] “The custom is for the wicks to be new each night”
 The reason: As on each night a new miracle occurs. Alternatively, the reason is because this is in memory of the Temple lighting in which new wicks were used daily. [Poskim ibid; See Menachos 85a; Rambam 12]
 Mishmeres Shalom 48:3
 The reason: In order so one does not decrease in the holiness of the wick which was lit first on the previous night. [ibid]
 Bezel Hachachma 4:128
 The reason: As it is permitted to use the wick after the 30 minutes have passed for even mundane matters. Hence, certainly it is permitted to use it the next night for a different candle. [ibid]
 Sefer Haminhagim p. 160 [English]
 Toras Menachem 15:303 [printed in Shulchan Menachem 3:271]; Shevach Hamoadim. p.102. Although Sefer Haminhagim p. 160 [English] writes based on a Sicha of the Rebbe that the custom of the previous Rebbe was not known, nevertheless, in the later years the Previous Rebbe’s custom was verified to be as stated above; See Hiskashrus 752 footnote 77; Chikrei Minhagim 3:230
 See Hiskashrus 596:17; Chikrei Minhagim ibid footnote 7