I can't view your SW file now, future version.
Can you click on the invincible face(s) as if they are still there showing an outline of the face edges? If yes, your graphics card might be wigging out.
Or does it select the face(s) through the part on the opposite side? If yes, the file or some feature(s) within the file are corrupt and need to done again. If the invincible face(s) are just created from a fillet and easy to do over again, roll back just prior to that fillet feature, create a new fillet feature that is identical, delete the "corrupt" fillet feature, and see if things change. Or might need to add that fillet feature after the mirror body feature.