A stand-alone sukkah is exempt from mezuzah as it is a temporary dwelling. The status of a room that one dwells in year-round and replaces its ceiling on Sukkot with schach is a matter of controversy.
Some authorities write that during Sukkot it is deemed a temporary dwelling because he is then living specifically in that room only because of the mitzvah.Also, in the short time between removal of the ceiling and the placement of the schach, the room might be seen to lose its independent obligation in mezuzah. Therefore, your son’s question is a legitimate one. Indeed, some authorities recommend removing after the ceiling has been replaced and replacing the mezuzah without a berachah,
Nevertheless, the custom follows those opinions that assert that such a room retains its status as a permanent dwelling, and consequently the mezuzot do not need to be replaced. They also reason that since the mezuzah was originally placed properly, it maintains its status even when some external factor exempts the room for a time.
 Shulchan Aruch Y.D. 286:11.
 Agur B’ohalecha 41:17:43.
 Agur B’ohalecha 16:31:72.
 Sha’arei Teshuvah O.C. 627:7, citing Pri Chadash.
 Pitchei Teshuvah 286:14, citing Arba Turei Even; Chut Shani, Sukkos p. 204; Igros Moshe O.C. 5:40; Aruch HaShulchan 286:27; Agur B’ohalecha 16:31:72; Mezuzas Melachim, Halachah L’Moshe 131; Kuntres HaMezuzah 139. Cf. Mishnah Berurah O.C. 626:21.