The Rokeach § 219 (brought by Eliyah Rabbah 625:1) brings those who say that when Rabbi Akiva (Sukkah 11b) says that Sukkos commemorates the sukkos that the Jews dwelled in, it's referring to when they fought against Sichon and Og (Numbers 21:21-35).
Eliyah Rabbah (basically the same as what the Rokeach himself writes):
והרוקח הלכות סוכה סי' ריט כתכ כשצלו על ארץ סיחון ועוג ועל כרכים שבארץ כנען אז ישבו בסוכות, וזה 'למען ידעו וכו''
It sounds like the time that they lived in sukkos was specifically while fighting Sichon and Og (or at least it started at that time).
Why would this be? In general I would ask why would they be in sukkos if they had the Clouds of Glory protecting them (which everyone agrees with, just Rabbi Akiva says that's not what the holiday of Sukkos commemorates). But assuming they were dwelling in sukkos, why was it only during this time period?
My only guess is when Aharon died, the clouds dissipated (inter alia Rosh Hashanah 3a (brought by Rashi to Numbers 21:1), Taanis 9a). That's when they needed to build shelters. Ta'anis says that the Clouds of Glory returned in the merit of Moshe. It doesn't say when. Perhaps it was after they fought Sichon and Og (which happened seemingly soon after Aharon died (Numbers 20:22-29).
Does anyone explain this Rokeach?