[Steve A]

Orbits around a spherical body can be calculated exactly by the point source method. Since the Earth is not perfectly spherical, there are some minor perturbations that cause the orbit to wobble a bit. The basic size and shape of the orbit do not change, it just wobbles like a top.
If the Earth was replaced by a black hole of the same mass, everything in orbit would stay in orbit. The gravitational forces caused by one earth mass at a fixed distance from the center of mass will not change just because it is converted to a black hole. It will actually probably Last longer because the air resitance would be removed.
Of course, whatever caused to Earth to become a black hole may have some slight impact on the orbiting satellites.
Steve