Four year old HDR-CX7 gives perfect picture quality but, recently, if allowed to run more than (perhaps) 10 minutes, device becomes hot and autofocus fails subsequently giving blurred images. Overnight cooling will produce perfect images the following day.
It sounds like a Steadyshot malfunction. Excessive Steadyshot vibration can occur when the camera gets warm through prolonged use; I think the blurring is due to the over-action of the Steadyshot mechanism, rather than an autofocus issue.
Try switching Steadyshot off and see if that helps.