737 CAT II
737NG is approved for CAT II dual/single autopilot and F/D approach under some requirments mentioned in the AFM (2 HYD system, 2 Elec. power sources, 2 ADIRU's, both engines...etc)
So after the stabilization 1000ft AGL stabilization gate and before the Alert height, you got a failure in one of those equipments, and you can control the A/C. My question here is you wait until the minima and decide.. or just iniate a G/A?