These are trainers that will battle you every time you re-enter the route/room/water after first going through a door then coming back out. I only know a two right now but I would appreciate a list of the others.
Route 4: Pokemon Breeder Irene
Lostlorn Forest: Pokemon Breeder Galen
There are 5 Pokemon Breeders in B2/W2, but according to Bulbapedia, only 3 will battle you again.
Pokémon Breeder ♀ April - Route 6
Pokémon Breeder ♀ Irene - Route 4
Pokémon Breeder♂ Marcus - Route 7
I'm gonna check the other Trainer classes