I haven’t been able to reproduce this, but I did notice that your “eye” tools look like they are from the ZB sphere primitives with the poles on the end. Geometry derived from the parametric objects can be problematic in a number of operations, especially if the operations overlap those poles, resulting in unexpected behavior.
Convert your eye objects to fully welded polymesh geometry first, with dynamesh. Then run it through zremesher if you need cleaner topology. Subdivide as needed. Perform your extracts from the remeshed spheres.
In a situation where you absolutely require the precise topology those primitives give you, you must first “prepare” the sphere by running it through tool>geometry>Modify topology>Weld Identical points, and then Tool>Geometry>Mesh Integrity>Fix Mesh. Easier/more reliable to just remesh them.
Perform the extract on a single eye (the left one), and mirror and weld (tool> Geometry> modify topology>mirror and weld) it to the other side. If it’s mirroring the wrong side, use the Tool>Deformation>Mirror command to flip it to the other side first, then M&W. This will be less error prone than having symmetry on during the operation.
Finally, I’m assuming by “clearing the mask” you mean you’re using the Tool>Masking >Clear Mask function, or Ctrl-dragging a mask marquee in empty canvas space to clear. If otherwise, please specify.