I have seen this problem with other Canon EF lenses and it went after repairing the faulty focus, looks more like lens problem for me, I suggest you send the lens for repairs.
Once you get your lens back , retest your lens for focus accuracy since the guys at Canon will kindly repair/replace the faulty part but they won't necessarily do focus calibraton
Once you get your lens back , retest your lens for focus accuracy since the guys at Canon will kindly repair/replace the faulty part but they won't necessarily do focus calibraton