All very interesting stuff but we seem to have drifted away from the original posters question!
The original question was about the use of autopilots when there is a system failure or some other abnormal situation that does not preclude the use of autopilots.
I believe that during abnormal situations if autopilots are available then they should be used where possible so that the crew can sit back and properly assess their situation and then make the correct decisions. Thereafter it may well be prudent to handfly but this would depend on the nature of the abnormality.