A/T and AP Disconnect logic.?

Was wondering ....after a flight into severe turbulence and CB's..when does the AP and A/T disconnect, as I usually ALWAYS hand fly the final, this time around the stick shaker sounded and the A/T could not keep the commanded speed....so I flapped it (non aviation term) and disconnected AP and A/T and hand flew a bit earlier than I would...My question is how severe does the turbulence need to be before the AP and or A/T disconnects?? ..to simplify whats the limits of the AP and A/T????.