Animation seems to be switching layers and I can't control it

I'm making a 2D game where a sprite continuously animates, but despite my setting the layers for it and fiddling around with the z coordinates for it and other sprites, the animation seems to be switching between different layers so that it flickers in and out of other sprites when it is being overlapped by another sprite. I've attached an example.

Does anyone know how I can fix this?

 

Hey,

The image link seems to be dead.

The sprite sorting order is prioritized over the object's z-coordinate, so you shouldn't have to touch those at all if your sprites all have different sorting orders.

Make sure that you haven't accidentally set sorting order keyframes that you didn't mean to in your animations. If you're using autokey, it's easy to accidentally set keyframes that you may not want, and that could cause the sorting order to be wrong.