If on Shabbos or Yom Tov the Sechach blew off due to wind, may it be replaced?[1]

No. It is forbidden for a Jew to replace the Sechach on Shabbos or Yom Tov.[2] This applies even if only part of the Sechach blew off or folded over, nevertheless one may not spread it back onto the Sukkah [even with a Shinuiy].[3] [Likewise, seemingly one may also not place non-Kosher material over the now empty space for the sake of achieving Dofen Akuma and making the Sukkah valid.] However, [if there is no other Sukkah available[4] then] one may ask a gentile to replace the Sechach for him even if the entire Sukkah fell.[5]

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[1] See Kaf Hachaim 637:5; Piskeiy Teshuvos 626:10; Nitei Gavriel 62:16; 18:7-8

[2] P”M 630 A”A 19; Shut Magidos of P”M 109; M”B 637:1 in name of Pischeiy Olam 637:2 in name of Shoel Umeishiv Reviah 3:25; See Admur 315:1; Michaber 315:1; Shabbos 125b

The reason: This is forbidden due to both the Ohel and Muktzah prohibition.

[3] M”B ibid; Pischeiy Olam ibid; Shoel Umeishiv ibid; Kaf Hachaim ibid

The reason: It is forbidden to replace the Sechach due to the Ohel prohibition. [See Kaf Hachaim ibid] Now, although it is permitted to add to an already established Ohel of a Tefach, this only applies by a temporary addition, however the addition of Sechach during Sukkos for the sake of a Mitzvah is considered permanent. [See Meged Yehuda on Shut Magidos 3 of P”M 109]

Other opinions: Some Poskim rule that if there remains a Tefach of Sechach that was no blown off, then one may replace it with a Shinuiy. [Nitei Gavriel 18:8; Vetzaruch Iyun Gadol how he ignored all the above Poskim!]

[4] Shut Magidos of P”M 109 [See also P”M 626 A”A 8]; Kaf Hachaim ibid; Nitei Gavriel ibid; Omitted from M”B ibid, Beir Yitzchak 13

[5] Implication of P”M 630 A”A 19 regarding Yom Tov, brought [and negated] in Kaf Hachaim ibid [unlike P”M 626 A”A 8]; Shut Magidos of P”M 109 regarding even Shabbos; Birkeiy Yosef 626:11; Lev Chaim 2:109; Pischeiy Olam ibid in name of Beir Yitzchak 13; Bikureiy Yaakov 626:11; Ateres Chachamim 6; M”B ibid; Piskeiy Teshuvos ibid; Nitei Gavriel ibid; See Admur 586:24; 594:2 and Chapter 3 Halacha 4

Other opinions: Some opinions question the allowance to even ask a gentile to do it on Shabbos or Yom Tov, due to the prohibition of Amirah Lenachri, as perhaps the placing of Sechach on the Sukkah is a Biblical prohibition. [P”M 626 A”A 8; Kaf Hachaim ibid] Other Poskim rule that it is only permitted on Yom Tov and not on Shabbos. [See Beis Yitzchak ibid; Piskeiy Teshuvos ibid]