B737-300 QRH SG Failure. Do not enage the autopilot.
Page 10.2 of the B737-300 QRH is headed "SG Fail"
After taking the QRH actions there is a line that states "Do NOT engage either autopilot" The word NOT is in capitals indicating a serious matter.
No explanation is given and I am unable to find out why the autopilot(s) should not be engaged. Appreciate ideas.
Also in RVSM airspace you need an autopilot. Otherwise altitude penalty applies. If critical on fuel this could be embarrassing. If say the captains SG fails, you may be faced with the situation (however unlikely) that it may be essential to not operate the EFI transfer switch in order to theoretically have one autopilot engaged and still meet RVSM requirements. In other words accept that the captains EADI and EHSI stay blank. Of course that brings with it more problems re flight instruments for the captain - but worse still could be fuel consumption at the lower altitude if forced out of RVSM.