The 737 only does auto go-arounds on condition that you are performing a dual channel approach, on hitting TO/GA one auto pilot is knocked off and the remaining autopilot takes over the go around
Actually both AP remains engaged in pitch mode until missed approach altitude is captured or another roll mode is selected. Both provided that sufficient time has passed for the stabilizer has returned to normal trim, otherwise - oh god - the
pilot has to
fly the aircraft manually! A dangerous beast such a 737, not suitable for modern day Commercial Air Transport, since "Todays aircraft are NOT designed for manual flying as we used to know it."
