If the Schach or a portion of it fell/flew off during Shabbat/Chag, can it be placed back?
Schach is muktzeh therefore cannot be fixed by a Jew during chag or Shabbat, but can be fixed during hol hamoed.
See for instance this digest of Sukkot laws
If Schach blows out of place on Yom Tov, one may not fix it, since the Schach is Muktzeh. However, if the Sukkah is no longer Kosher (or its status is questionable), one should consult with a Rov as to whether a [non-Jew] can fix it.
or what dinonline writes here
There is no problem in fixing the sechach during Sukkos. This cannot be done on Yom Tov, but only on Chol Hamoed. On Yom Tov, it can be done by hinting to a non-Jew.