I have seen this happen. In my case it was caused by my old yoke. When centered, the yoke was not really centered; a noisy sensor was commanding a bit of pitch up or pitch down. The autopilot was fighting this. If you go into the calibration setting for your stick/yoke and click "Add Response Curve" for pitch, you will be able to see if and how much pitch input (a blue x/y plot labelled 'Current') is being commanded while the stick/yoke is in neutral. You can then add a point to the curve just beyond this and set it to zero, effectively creating a null zone to null out the false pitch commands.