Yes, there are standards and it's up to the bishop to revoke the university's status. There are several that have been warned in recent years - Holy Cross, Boston College, Georgetown, etc. The ones that get themselves into hot water are the ones run by the orders, not that there are many diocesan colleges and universities. And most of them are actually run by lay boards with a priest as president or chancellor. There are a few good ones out there, but none of them seem to have a winning Division 1 basketball program, which is why they aren't household names.
It retains its Catholic status by the weakness of the bishops and the pope. And by their failure to address the infiltration of Cathholic universities by anti-Catholic secret societies. The 1967 Land O’Lakes conference on modernizing and secularizing Catholic colleges basically castrated Catholic intellectual culture and Catholic identity at American Catholic universities by turning them over to liberal non-Catholics and modernist heretics, making that a goal. Although there have been statements of protest from time to time very few bishops have done that much to address this or to explain the nature of the problem.