I do not understand fully how to gyro work?
Have you played with a toy gyro? When you rotate it you feel a resistance to that movement. That resistance you feel is translated into a voltage. If you stop moving it, you will stop feeling the restoring force and will stop producing a voltage. So yes it is working normally.
However, I don't know about your specific problem, does the gyro have three axis readout? Some only have two and I can't find a data sheet on line. Can you point me towards one?