Many air to ground/air radars (as in fast jets) use pulsed doppler radars that use the change in speed of the return pulse compared to the sent pulse to identify moving targets (high threat). These radars often have a lower limit set to take out relatively slow ground targets like traffic; if the limit is 40 kts for example and you are doing 30 kts your return will be processed out. If you are moving faster but at a constant distance from the radar head then you will not be seen as you have no velocity relative to the direction of travel of the FJ radar - this is known as the ZD notch (Zero Doppler).
I don't know if ATC use pulsed doppler radars nowadays but if they do then similar rules would apply.