The visibility of the signal depends on the full scale setting - if its 2000 deg/s then simple hand movements are likely to be at a few percent at most of full-scale and if there is no low-pass filtering enabled there will definitely be noise... It could easily be misbehaving, but it would be a shame to miss the signal by not looking carefully. Programmable LPF and full scale settings on some MEMS chips mean they can be set up so the signal is not very obvious.
The integrated version of the signal is much easier to observe since it is not evanescent when you stop turning the device and noise is being averaged.