In Pokemon Emerald, a PokeNav feature called Match Call was added that allows you to keep track of certain NPC trainers and see whether or not they're available for a rematch. The trainers who are available for rematch at the moment have a tiny Pokeball icon next to their name:
Battling with these trainers will remove the icon from next to their name. It seems like only a finite number can be available for rematch at any given time, so it's necessary to battle some of them in order for others to become available.
I know that trainers who are not or cannot be registered typically cannot be battled again, but it seems like some trainers registered on Match Call, such as Young Couple Kira & Dan in the Abandoned Ship, are never available for a rematch. Others, like Triathlete Abigail on Cycling Road, are sometimes available. Is there anything that can be done to rematch trainers like Kira & Dan? If not, which trainers that are registered on Match Call will never be available for further battle?