There are no published criteria, so all you will get here will be individual data points and common sense. The members posting data points will not have all the information available to AA when the decision was made, so the data points will not be particularly helpful, leaving you with just common sense answers. For example, if the outbound flight is the last one of the day, and the inbound flight was delayed for reasons that would cause AA to pay for overnight accomodations and meals, AA is more likely to hold the outbound.