And while I have not yet had a chance to talk to a 737 pilot, I did
have
a chat with a 757 pilot yesterday and asked him how long a 757 would
remain stable with the autopilot off. He looked at me like I was
crazy
for asking the question (and rightly so) and said "not very long."

How long is "not very long"?

I actually pressed him for details because I knew you would ask this.
He said several things. First, he said he didn't really know because
he'd never actually tried it. Company policy forbids disconnection of
the autopilot in cruise. The airplane is unstable enough that doing so
is actually potentially dangerous. To keep the plane flying safely
without the autopilot at cruise requires constant attention. An
autopilot failure in cruise (unlikely because there are redundant
autopilots) is an emergency which requires immediate diversion to the
nearest airport.

Bottom line is that a 757 handles not much differently from any other
heavy, clean plane. In perfectly smooth air if you have it perfectly
trimmed you might have a minute or two at the outside. Under realistic
conditions (a little turbulence, less than perfect trim) you have a few
tens of seconds before you are in an unrecoverable roll. In bad weather
you could be unrecoverable in only a few seconds, but that would be
unusual. It's not like a helicopter where if you take your hands off
the stick for a few seconds you're pretty much guaranteed to die.

He also said you'd get altitude excursions sooner than roll excursions.
This is consistent with my personal experience which is that as planes
get faster (and my personal experience covers a range of 90-180 KTAS
cruise speed) they get harder and harder to trim for pitch.

I really hate being on the (apparently) same side as our favorite troll, but
policy requirement to cruise only on autopilot is more likely related to the
tight altitude tolerance under RVSM. After you scale the weights involved,
the greater distances, and the air density at typical cruising altitudes, I
suspect that the flight attendants pushing the beverage cart up the isle
would be more than enough to bust the airspace...

Peter