Hi,
first of all, were are you disengaging the A/T? on the MCP? If you do it on the MCP tis is wrong, only used for non-normal procedures.
A/T dissengage is done via the litte knob on the thrustlever.
It should be possible to override the A/T anytime by hand or you press the button on the thrustlevers.
Press it one time to get the A/T hold mode, second time for disengage.
For your problem with dropping Airspeed, in any mode, expect A/T off on the MCP, you will have the socalled wakeup-mode active, in this is airspeed is to slow A/T will connect automaticly when you airspeed becomes to low.
regards