The reason why you want to keep the AP on in severe turbulence
 

According to Airbus..."Recent severe turbulence events have clearly illustrated that potential consequences have been minimised thanks to the appropriate use of automation by the crew, mainly in keeping Autopilot engaged instead of possible instinctive reaction, which is to take over manually.Keep Autopilot engaged. Indeed, detailed studies regarding aircraft behaviour when crossing such external perturbations has shown that the less the aircraft reacts at short term to the turbulence, the better it is. Indeed, the dynamic of such severe turbulence is so, that any additional pitch down reaction to counter the initial up draught will accentuate in most cases the pitch down effect of the down draught usually subsequent to the up draught. This will accentuate the excursion in negative load factor and so increase the risk and number of injuries. To minimise the additional effect of such pitch down order coincident to the down draught, it is recommended to the crew not to react to the turbulence by short term side stick inputs corrections and to keep Autopilot engaged."

So basically, your pitch control inputs get out of sync with the aircraft reactions making things worse.

Mk 1 Airbus had a TURB mode for the autopilot which (IIRC) reduced the response rate to deviations from the flight path. Do the modern AFCS have such a mode?

I am guessing the average pilot is unable to do that in severe turbulence and therefor the AP does a better job.

Even the venerable 146 had Turbulence mode. It just maintained a pitch attitude and rose and fell with the currents. No RVSM though!!

According to Airbus, they have modified the flight control software so that it is less likely to disconnect in a turbulence encounter(autopilot robustness). It would be interesting to know if this mod is on all aircraft or is just an option.

"Flyby-
wire aircraft
A severe turbulence may lead to excessive high
speed excursion (beyond VMO/MMO) or to
excessive low speed excursion (below ‘alpha prot’,
angle of attack threshold of alpha protection law
activation). This will induce Autopilot disconnection
and activation of the appropriate manual flight
control law (The VMO/MMO protection or the angle
of attack protection that will command respectively
pitch-up and pitch down movement to reduce
these excursions).
In order to keep the Autopilot engaged as long as
possible, flight controls software modifications
have been developed on fly-by-wire aircraft. They
make the Autopilot more robust to disconnection
resulting from a transient VMO/MMO or ‘alpha
prot’ exceeding subsequent to a severe turbulence.
Autopilot robustness improvement in case of
transient ‘alpha prot’ angle of attack exceedance
has been already implemented on all in-service
fly-by-wire aircraft.
Autopilot robustness improvement in case of
transient VMO/MMO exceedance has been
introduced as shown in various flight control
software."

FOs leg me as PM on A330. Hit turbulence and AP disconnected, very unusual for A330. FO flew manually and left AThr in. He chased altitude, within 3 cycles the pitch attitude was getting bigger as he overshot the datum on the way up and down and the Thr was out of sync (going down thrust increasing, going up thrust decreasing.)
Moral: PM monitors, advises and if need takes over (not required this time) FLY ATTITUDE if AP disconnects, remember thrust setting for stable flight, set it and disconnect AThr.

No, but doesn’t the aircraft maintain the current ‘attitude’ when you disconnect the AP?

Extract from the B737 FCOM Supplementary Procedures Adverse Weather:
Severe Turbulence.
Yaw Damper....On.
Autothrottle… Disengage.
AUTOPILOT....CWS.

The problem with hand flying in severe turbulence is the risk of pilot overcontrolling. Pilot induced oscillation is a common characteristic and this can be critical at high altitude. Automation dependency can make things worse where reversion to hand flying by pilots lacking the necessary competency often leads to pilot induced oscillation. Some pilots are worse than others.

Large and rapid movement of ailerons not only causes unwanted spoiler operation but throw in unnecessary movement of the elevator and rudder in response to large scale excursions caused by gusts, and the stage is set for pilot induced unusual attitudes. Hence the Boeing 737 advice to use autopilot CWS where the pilot is still in control but the controls are far less sensitive and more resistant to inappropriate manual inputs.

So it all boils down to individual pilot manual handling skill; especially in severe turbulence encounters in IMC. Instrument flying skill is paramount and some pilots don't have it. . Nowadays, where the accent is more on full use of automation than basic handling skill, it would be wise to accept the autopilot can usually do a better and safer job than a rusty pilot wrestling with the controls.

Indeed; there need be no ‘wrestling’ of the controls. In severe turbulence the danger is that some pilots might much too aggressively attempt to keep the aircraft, straight, level, and at the same altitude. By doing so, they might over-stress the airframe, for example the ?A300 that had its fin snapped off, (due to pilot action), during a wake turbulence encounter.

In Airbus FBW with the autopilot out; feedback loops, (not on the A300), will generally try to maintain the basic attitude, but large disturbances will require the pilot to gently return the attitude datum. But altitude is not the most important parameter until clear of severe turbulence.

Also having experience of how your aircraft handles at altitude helps in these moments - But that's not helped by RVSM mandating autopilot usage...

Whatever happened to soft altitude mode? In Safety First there is a series of control your speed from take off to landing. It should provide most answers. In Airbus most problems have occurred by switching off the AP. Airbus recommends AP on and manage speed excursions with speed brakes and only if ATHR behaviour is not satisfactory then use manual thrust. Even in windsheer if AP is on it should not be disconnected. AP will disconnect with speed excursion or Valpha prot. Only then it should be manually flown.