Though, AF447 isn't a simple case of the plane being under direct control. When the two pilots give conflicting inputs, Airbus silently averages out the two inputs. The pilots were confused as to why their inputs weren't seeming to work, then the pilot who was trying to do the wrong thing (pull up) figured out why his inputs weren't having any effect and hit the button to silently ignore the input from the pilot who was trying to do the right thing (nose down). As I remember, it was the more experienced pilot (captain) who was correctly trying to get the nose down, but it seems he never figured out why the plane wasn't responding to his inputs.

Also, when they went very far into stall, the stall warning disabled under the assumption it was a sensor problem rather than the airplane actually getting into that bad of a stall. So, paradoxically, starting to improve the situation caused the stall warning to come on, while doing the wrong thing caused the warning to go away.

Both pilots were trying to debug with information intentionally being hidden from them. (Honestly, the stick should vibrate or something if your inputs are being ignored or counter-commanded by the other pilot. Better yet, mechanically link the controls as in Boeing planes... it's not great that the stronger pilot wins, but at least both know what's going on.) Granted, there was a lot of pilot error in AF447, but there were multiple user interface issues that greatly contributed to the problem.

Edit: Also, as I remember, the start of the incident was that the pitot tubes iced up and the autopilot disengaged itself because it had no idea what to do. It's hard to point to a case where the automation has explicitly given up as a case where we should rely on more automation. Clearly a world where the automation was better would have been better, but just letting the autopilot do its thing wasn't an option. The autopilot disengaged itself.