One of the biggest issues is using too wide of a lens aperture at close distances! If you are close enough for the eyes to be a major, large-sized part of a picture, then there needs to be enough depth of field to render them sharply. It's simple: when in-close, stop the lens down to f/5.6 to f/11, somewhere in that region,and magically your photos will have sharp eyes, and probably a sharp nose as well.
Most of the time, beginners misunderstand that at CLOSE distances, smaller apertures, like f/5.6, f/6.3, f/7.1, or f/8, will give great results on a close-in face AND the background will also be adequately out of focus and blurred; shooting at f/1.8 to f/2.8 is not usually a good idea at distances where a face is close-up, and where missed focus will be noticeable or distracting. Again, when you have the camera close enough for the eyes to be a major part of a picture, it makes sense to render them sharply, otherwise the picture will be spoiled, so stop the lens down to an appropriate f/stop for the kind of photo you want to end up with.
When you shoot close-in, and the depth of field band of the lens and f/stop in use is so narrow that focus is critical, the easiest thing to do is to work with a 4 to 5 inch deep DOF band, and that means stopping the lens down a bit. The closer the camera is to the subject, the more error there is in the center-focus-and-recompose method; as distances grow a bit longer, focus and recompose becomes more useful, and less prone to focus errors. One basic issue is shooting close-in, using focus-and-recompose, and then placing the eyes off-center at the top of a tall-framed image: being on a diagonal line from the center of the sensor, the distance to the eyes will be LONGER than the distance from the center of the sensor, and the focus will be off by more than the depth of field band can possibly cover. This is why focusing with an AF square that is closest to the desired focus point works so,so well at close distances!
Try focusing on the ear with the center AF bracket, and then recompose when inside of 10 feet.