לזכות ידיד נפשי הרב משה גבריאל בן יהודית הוא וביתו וכל אשר לו לברכה והצלחה!
The gemara [Succah 7a] says that if one lays schach over an open mavoi [alleyway] that has a lechi, the succah is valid. Since [מגו] the lechi is regarded as a wall with respect to Shabbos it is so recognized with respect to the succah as well.
The gemara leaves a lot of room for interpretation [and 'blog'ation]. WHEN is this succah kosher? All of succos? Only on shabbos? Otherwise?
Rashi says that it is a valid wall on shabbos only but not on the weekday. This is logical. Only on shabbos do we regard it as a wall so it makes sense that for a succah we only view it as a valid wall on shabbos only.
The Rif dif's [differs] with Rashi. He says that it is a kosher succah wall all seven days and not just on shabbos.
The Rambam seems to agree with Rashi that it is only a wall on shabbos. The Maggid Mishna says that we can derive this understanding from a careful reading of the gemara. The language of the gemara is יתירה שבת דעלמא על שבת דסוכה - [The criterion for walls which permit carrying on shabbos in general is more stringent than that which permits carrying within] a succah on shabbos [see the gemara there for context]. It is clear then that Rashi and the Rambam are correct and that we are dealing with a lechi in a succah on shabbos only.
The Rogochover in his commentary to the Rambam takes a different approach. He says that once shabbos arrives, this lechi is considered a wall and doesn't lose that status even after shabbos ends.
Ki-darko bakodesh - he brings a proof from a totally unexpected place. In Bava Basra [153b] we discuss the halachic status of a valley surrounded by a wall. The law is that in the summer, it has a din of a reshus hayachid with respect to the laws of shabbos [since it has a wall] and a reshus harabbim with respect to tumah [since it has no produce growing and people walk there. Thus, a sefek tumah is tahor like it is in all reshuyos harabbim]. In the winter it is considered a reshus hayachid both with respect to shabbos and tumah [since produce is growing, people don't generally walk there and safek tumah is tamei].
Rashi there adds, that once the winter comes around and the valley adopts the status of a reshus hayachid, it retains that status forever, even in the following summers.
So we see that once we apply the law of reshus hayachid, it stays that way. We may extract from here that once shabbos passes over the succah and the lechi adopts the status of a wall, it will remain that way even after shabbos ends.
Pilei plaos!:-)