Sorry, since the feature is somewhat obscure, I should've laid out more specific steps to reproduce.

1) Start one of My Pet Dungeon missions

2) Switch to "My Pet Dungeon Tab" in the UI

3) Click on "lvl 1" label in that tab, notice a lock icon apperaring on top of it

4) Enable automatic wave spawning in the same tab

5) Kill spawned enemies, notice that the next wave is spawned as level 1 as well

6) Save the game and load back immediately

7) Switch to "My Pet Dungeon Tab" in the UI again

8) Notice that now there's no lock icon on top of enemy level indicator

9) Also notice that automatic wave spawning is still enabled

10) Realize how bad things would go if you didn't check this right after loading the game :)

Err, sorry, did not expect that login button will also submit the form.

So, yeah, locking enemy level in toybox is not persisted, at least in autosaves. Automatic wave spawning is though, so loading from save can result in enemies getting stronger when they shouldn't.