How difficult is it to hand-fly a jet at cruise altitudes? Other than autopilot failure and just doing it for the fun of it, when might you want to hand-fly at those altitudes?
I suspect the answer to the first question varies with different aircraft. I have an answer for the 747-100 and -200 series below.
For 747-100 and -200 aircraft at 35,000 ft and above, you can do it, but it's hard to keep the airplane within 100 feet of the assigned altitude, and you typically can't do that (or at least I couldn't) without practice. 200 foot altitude excursions were the norm when I first took control if I had not done it for a while. For the few first officers that accepted an invitation to try it, an initial 300 foot altitude excursion was typical when they first tried it, especially immediately after disengaging the autopilot.
I found the concentration required was very tiring. Ten minutes was typically enough to satisfy the urge.
Insofar as when you might want to do it, I found hand-flying produced a smoother ride in heavy to severe turbulence than the autopilot's turbulence mode, which tended to try to keep the assigned altitude and aircraft pitch too slavishly.
It's probably not a good idea to hand fly jets at cruise altitudes in many cases (US, EU, and others). The reason is that from FL290 to FL410 (29,000 to 41,000 feet standard pressure altitude), a lot of airspace is under RVSM rules (Reduced vertical separation minima).
This means that aircraft are only separated by 1000 feet vertically. One of the requirements for flying in RVSM airspace is a system for automatically maintaining altitude. If this system is not working, either the aircraft must fly at an altitude outside RVSM space (most likely below) or ATC must agree to provide 2000 foot separation above and below from other traffic.
Some examples of this in practice:
See the related question for more details:
Is it legal to fly in RVSM airspace with an inoperative autopilot?
Aerodynamic damping is proportional to density, so all maneuvers require less control input at altitude than near the ground. On the downside, excursions from the trimmed condition produce greater amplitudes before stability pulls the aircraft back. This explains why hand-flying needs more attention at high altitude.
Background: Damping is the reaction of a system to movement, and positive damping means the reaction slows the movement down. Case in point: The horizontal tail. When the pitch attitude changes (say, by a vertical gust which changes lift first on the wing, then on the horizontal tail), the rotation of the aircraft around the Y axis (the one pointing sideways) creates an additional vertical speed on the horizontal tail surface. This vertical speed is proportional to pitch speed (obviously) and the distance between c.g. and tail. This speed changes the local angle of attack by the ratio between the vertical speed and flight speed. Now we are at the core of it: A high flight speed will cause a smaller angle of attack change at the tail for the same pitch rate. Since this angle of attack change creates the damping force (by creating lift on the tail which counteracts the pitch movement), a higher flight speed at the same dynamic pressure will lead to less damping. This is a fancy way of saying that flying in lower density air makes the aircraft more responsive to disturbances.
