As far as I can tell - activation of the stick pusher does not turn off the 727 Sperry AP in my 727.  

I think I have determined two causes of the excursion into a deep stall.   One is pilot error - the other is ???

Flying below 10000' at about 190 knots using the AP in ALT HOLD and HeadingSelect.  Change the heading bug for a 90 degree turn.  The AC enters a standard rate turn.  If the turn continues long enough - the airspeed keeps dropping if I don't increase throttle - eventually drops below Vs with AoA (I did ask it to keep a set altitude) ever increasing.   This is just bad piloting.

I have done lot's of testing at FL32 and find that I can enter a DEEP STALL if the AoA exceeds 16 degrees and Mach drops below .48 - now why does it do that?

I think it happens when I have a GPS on the 2nd monitor.  I am making keyed inputs into the GPS, e.g. new VOR, and the FSX or 727 program sees those as inputs to the AP or throttles.   For example I was typing in the new VOR and the AP disconnected and the throttles rolled back from 80% to 20% - I let the problem progress and soon the plane was pitched up at 16.8 degrees, IAS was 114. MACH was .45 and vertical speed rapidly approached -10,000.  

All this occurred when I typed NID into what I thought was the GPS but  it acted like the focus was still on the VC so the NID was taken as input to the ???

While testing the Deep Stall I just saw IAS=265, MACH=.58, AoA 1 degree up and VSI=-6000.   This was during recovery while I was trying to bring the nose up without overstressing the plane.  

So - I think my Mach.71/IAS 140 must have been during the recovery - before I understood the problem.

However,  the 727 VC gets in a situation where the MACH and/or the IAS jumps suddenly either UP or DOWN and often not in synch.  The ADI also goes from horizontal to vertical (on it's side as if OFF) at times and stays like that for many seconds - then spontaneously reverts to a normal horizontal display.

The problem comes and goes but gets progressively more frequent - the only way to stop the problem is save the flight, exit and restart FSX.

My last observation is that the AP does capture the VOR in NAV LOC and does EVENTUALLY get on track.  I have run a number of tests where I selected NAV LOC while approaching the desired radial at an angle of 10 or so degrees and three dots off the track.  The SPERRY AP in my 727 will overshoot the desired radial and then oscillate back and forth for several minutes before settling down on the course.  The oscillations can take it up to 3 dots past the desired track.  

But, if I leave it alone, it always gets on track after three or four minutes.