Drifting object between 2 keypoints

I have one object that follows a shape path, then is stationary for 2 minutes, then follows a different shape path. Either side of the stationary period are keyframes for position that are identical. However, the object very slowly drifts up 50 pixels and back down during the stationary period. The strange movement is also present after it is exported and processed by Media Encoder. This object covers a different animated object several times on another layer throughout the 2 minute period, so the shift is quite noticeable.

I have ensured that there is no other animation happening to the object in question, motion blur is off, and the anchor point does not change. What else should I check?