Why isn't the previous Battle Pass season in the Archive? When will it appear?

A season isn't added to the Archive the moment it ends — it appears one Battle Pass later. The season that just finished becomes available in the Archive only when the Battle Pass that's running now comes to an end.

For example: while Medieval Legends is running, the previous season, Outlaw Island, isn't in the Archive yet. It appears there once Medieval Legends ends. The season before that, Yo-Ho-Ho and a Bottle of Fuel, is already in the Archive.

If you bought that Battle Pass, it will show up in your Archive as already owned — you don't pay for it again, and you can keep unlocking the rewards you didn't finish.

If you didn't buy it, it becomes available for purchase in the Archive at the same moment.

Either way nothing is lost — the skins from that season stay available through the Archive.