A piezo disc is essentially a capacitor.
If there is a DC voltage on that capacitor, from e.g. pin leakage or clipping, then it could stay there.
A drifting or not defined (floating) pin.
Normally a (1Megohm) resistor is used across the sensor (pin to ground) to force the baseline to ground level.
But for a vibration sensor, you could bias the piezo mid-voltage (with a 2-resistor voltage divider).
A Due uses 3.3volt logic, so use one resistor from pin to ground, and one resistor from pin to 3.3volt.
Use equal high value resisors (1-10Megohm) if you also want to detect low frequency vibrations.
You should now have an A/D value of ~512 (or 2048) as baseline.
Leo..