In the Battle Tower/Subway/Maison/Tree, when in the win streak do opponents stop getting stronger?

Question

I noticed that opponents at different rounds use different movesets. They have to run out of new movesets eventually, right? Please don't question my curiosity.
Edit: I already have partial answers for the Generation 4 Battle Tower, Battle Maison, and Battle Tree. I'm only missing information for the RSE Battle Tower and the Battle Subway. Thanks to SadisticMystic for giving such a good partial answer and sorry for having to convert your answer to a comment.

Comments

In Battle Tree and Maison, there's a set of trainers that can appear in the first 10 battles (actually for Tree that's the first 9 battles, since every multiple of 10 draws from a "Famous Trainer" list instead of the normal list). After that, if you get to 11, they rotate some of the trainers off the list and bring in new ones, with what are generally perceived as harder movesets, and you roll from that list up to 19-20. At 21 there's another change-off, where all the remaining trainers who were still in the rotation from the first 10 get scrubbed from the list, and another new selection joins in. Likewise for 31. **In Maison, the last change to the list happens with battle 41**, and that's the point where some of the trainers being introduced will have legendary trios and such on their teams (discounting the Chatelaine herself for battle #50 in particular). Tree also uses 41 as the point to start adding trainers with legendary rosters, but **in Tree there's also one more rotation at 51**, right after you beat the Battle Legend. In fact, no one gets knocked off the list at 51, but a wide variety of trainers are added, including several more with "legendary spam" teams, so at that point you have to be ready to cope with all kinds of different team strategies.

https://bulbapedia.bulbagarden.net/wiki/List_of_Battle_Maison_Trainers#Super_Course_Trainers
https://bulbapedia.bulbagarden.net/wiki/List_of_Battle_Tree_Trainers#Battle_Tree_and_Battle_Agency_Trainers

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You know anything about the RSE Battle Tower or the Battle Subway?

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In the Subway, they stop getting stronger at 10. In the Maison/Tree, they stop at 20. I don't know about the Tower though.
Source: Experience

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In the battle tower new pokemon stop coming after the second palmer battle as that is when you can battle all pre-generated pokemon available in the tower, it may be similar in the other games.

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These might be helpful for Gen III:
https://www.smogon.com/forums/threads/battle-frontier-max-stats-pokemon-database.15426/#post-311777
https://www.smogon.com/forums/threads/gen-iii-battle-frontier-discussion-and-records.3648697/#post-8081012

Smogon says trainers will start using legendaries at battle 28 in the Battle Subway Super Courses. The latter two links show which trainers use which Pokemon at what times.
https://www.smogon.com/ingame/bc/battle_subway_part1
https://www.smogon.com/ingame/bc/bw_subway_pokemon
https://www.smogon.com/ingame/bc/bw_subway_trainers