I use this technique all the time with, like you, single point, dead center focal point. It's not the camera, it's something that you are doing - I don't mean that in a bad way toward you but it really is something you're perhaps not doing.

Okay. Focus on (in the case of this photo) on your lady's face. Do not release the half press and recompose. Her face will be in focus and in the light you had, she should be in overall focus. If you're not holding that half press when you recompose, that's the problem. If you're holding the half press but moving slightly, forward or back, that could be the problem.

As long as you hold that half press the focus and exposure are locked and cannot move.

Hope I helped... good luck