I think you're missing the point.
A rotating primary radar only detects aircraft because it's transmitting and receiving all the time, i.e. any time it's pointing at an aircraft it knows it's always going to get a reflected signal.
OTOH a rotating Mode S receive-only antenna, assuming it's directional, will by definition have a limited beam width and will only pick up signals if an aircraft happens to be transmitting a squitter or interrogation response during the period that the beam is pointing at the aircraft.
Say, for example, your antenna has a 20º beam width - that only gives you a 1 in 18 (about 6%) chance of picking up any given aircraft transmission, with the remaining 94% of transmissons happening while the antenna is pointing in the wrong direction. And that ratio will hold whatever rate you rotate the antenna at.
The answer, of course, is to have a much wider beam so that you can pick up most, if not all transmissions - 360º would be good :-)