As objects fall into black holes the wavelength of the light they reflect, and that your eyes collect, gets longer and longer. This means, its quickly passes the infrared region and is effectively black to your eyes. As the light gets longer, measurement devices can't detect the object anymore. So at the same time it gets 'stopped in time', it becomes part of the black hole.
Remember that the only correct picture of what happens near black holes is General Relativity. And GR is a mathematical description. All those thought experiments about falling objects, fall short.