In addition, once the Radio Tower has been saved, the player can call registered Trainers to arrange rematches with them without having to wait for the respective Trainers to call the player. Each Trainer has a specific time during a specific day each week where they will accept a rematch when called; if they are called at any other time of the week, they will use their usual script, and a rematch will not be arranged. When a Trainer is called at the appropriate time, as long as the player is not at the same route or location as the Trainer, they will accept the challenge of a rematch and can then be battled at their original location with higher-level Pokémon at any later point in time (though, once the rematch has taken place, the player will need to call or be called again in order to carry out another rematch).
source and list of rematch times
