Do you in fact mean Live Chess?
If so, then simply Block Member as soon as that kind of thing starts.
(However, remember that if you are both requesting a challenge with the same time controls and ratings range, that can serve to automatically put you two together if you both keep posting challenges. But, inasmuch as you said that your opponent is offering you a rematch but aborting, then he is serving to perpetuate the issue. Inexperienced players sometimes do this if they don't like the color that the server has chosen for then, not realizing that it is fruitless to fight that battle.)
This player keeps accepting my challenge for online chess with 1 min time limit. Then he aborts the game over and over. I can't get a game because of this. Then he started aborting and then offering me a rematch. When I accept the rematch he aborts again. Is there anything we can do to ban players like this? This seems like such a waste of time.