Good question. The aircraft starts to feel very eratic and you feel that the autopilot is no longer in control. I guess it's the same during take off, during those first couple of turns on assent you can feel the pilot making minor adjustments and you feel a varied degree of G force as if he/she uses the rudder a few seconds after the plane starts banking.
Same as landing, most flights I have been on are on budget airlines which need to get down quick, turn around and fly out again. I was thinking that most of these pilots use the autopilot until they are on finals, just to make sure there is no problems lining up or any other factors which may result in the plane having to go around.
Or it could be that I have got all of this wrong
Err, not quite. If the aircraft starts to feel "very eratic" I would suggest there is something wrong with it! Pilots are more than capable of flying the aircraft with or without autopilot. If you are flying a jet, or any large turboprop for that matter you will not be using any rudder in the turn. Rudder is only used (By the pilots) in an engine out situation or a crosswind during take off or landing. The comment re low cost carriers is also wide of the mark. So unless you hear the autopilot disonnect in the cabin, it is unlikely you will know when the autopilot is disconnected.