This issues has happened before. A layer appears differently (moved) on the CH stage, but appears to be in the correct position in AI and in CH rig window. Changing the position in CH rig window does not move where the layer is rendered in CH stage.
You'll see the gap between the eyelid and rest of eye in the CH recording stage image. This persists with vector rendering on or off and at all resolutions. Also tried moving the lid layer in AI to a newly created layer as this has helped before. No luck.
As a follow up, I wildly exaggerated the size of the pupil in Illustrator to get an idea of how much the lid artwork layer is being changed by CH... It's hard to tell, they seem about roughly the same size..
Another one for Adobe staff I suspect (like DanTull).
It looked a bit to me like the CH scene rendering was lower resolution than the rig panel.
Is the eye lid a different layer? I was wondering what the mesh looked like along the edges where the gap is, e.g. if zoomed in. Is the face warping very slightly and the eyelid is not, or some similar rounding error.
Only thing I can suggest is to make the layer slightly larger than required so there is a bit of overlap.
Oh, was this a media encoder output? Remember that the scene playback window is an approximation, not a true render. They simplified things for speed. The final render uses the more precise rendering is my understanding (And takes longer as a result).