If it is a dispute then the staff members should generally have a fast response to it as you might have been wrongfully banned. If it is an apology they do not have to respond fast. They do not have to accept it either. So in conclusion disputes must be dealt with fast but apologies can just stand there for ages.
Be sure to tag the staff member that banned you so they can get an alert about it. Also you cannot have a ban appeal that is a dispute AND an apology at the same time.