I'm not sure if there's intentionally a randomisation element now to whether or not pets are able to be successfully swapped but I thought I'd describe this here in case it's not intentional.

Today in the lost grove, I tried to swap pet 1 and 3 while fighting the earthbender but multiple times in a row it didn't work. I selected which pets to swap, they got the red target mark, then I selected which attacks to use and clicked end turn. And when my next turn started, the pets were still in their original positions, not swapped. I tried several turns in a row and eventually it did work and they did swap. This happened in the ancient crypt as well as in first floor south.

were the pets stunned at all? Stunning prevents switching

I don't think so but I'll keep an eye out for that if it happens again, thanks!

The Earthbender does indeed have an ability that disables a pet, which would prevent you from being able to swap positions until the debuff fades.

Gotcha. Probably just that, then. Funny, I've never experienced this happening before haha.