If on Shabbos or Yom Tov the Sechach blew off due to wind, may it be replaced?
No. It is forbidden for a Jew to replace the Sechach on Shabbos or Yom Tov. 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]. [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 then] one may ask a gentile to replace the Sechach for him even if the entire Sukkah fell.
 See Kaf Hachaim 637:5; Piskeiy Teshuvos 626:10; Nitei Gavriel 62:16; 18:7-8
 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.
 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!]
 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
 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]