This is a weird issue that only pops up on very specific skeletons, and apparently only when FlipX is true. I recently updated the Spine editor (3.4.02) and runtime (using Unity 5.3.4p6), which seems to have made it happen more often, but I do remember it happening once in a while before that.
When it happens, a SkeletonAnimation seems to be culled by the camera before it should be if it's right up against the edge of the screen, as you can see here:

The SkeletonAnimation looks identical in the editor and inspector (transform values, gameobject and renderer being active, etc) whether it's visible or invisible in-game, so I'm pretty sure it's some kind of culling issue:

I'm using 2D Toolkit, but the camera is a normal orthographic Unity camera. Just to be sure, I removed all my scripts from the object and it still happens.
Any idea what could be wrong here?