I had the same problem and replaced the fan and the fan clamp. It didn't seem to tighten up and it is not immediately obvious how the clamp secures the fan to the shaft.
In order to secure the fan to the shaft, the clamp has to be tightened VERY tight. This pushes the clamp down the angled face of the fan and thereby pinches the shaft to hold it in place.
In other words, a nut-driver won't cut it. Break out the ratchet or long wrench for this one. It needs the extra torque to hold the fan in place.
Unless your fan is broken (out of balance like mine was) you shouldn't need to get a new fan. Just loosen the clamp a bit (but don't take the screw all the way out) and then when the fan is back far enough, tighten the CRAP out of it.
PS> A big thank you to jfidler for the audio file. I knew right away this was my problem after hearing it.