That’s the “just say no” argument. It just isn’t effective.
The crosswind is a demonstrated limit, only a restriction if the operator’s SOP makes it so.
Am not aware LOP leaning is an AFM/POH restriction, although some engine service manuals may be more specific.
The A/P limits are restrictions.
I’ve moved the autopilot/OEI specific posts to this original thread.
Maybe if we knew why autopilots are proscribed OEI, we might be able to discuss it
Go for it 
With extra human help the autopilot can be made to work. i.e. rudder trim
I know nothing about twins but I do know how “classic” autopilots work: they have wings-level as the primary roll control loop (and that is what you get in the ROL mode), heading goes in next (and is used in all phases of flight), and the NAV error goes in after that (as an integral term, so eventually the track will be followed no matter how crooked the plane is sitting in the air). So if to hold a heading you need to fly with say a 5 degree roll, it will eventually do that. You can test this in flight by pushing one pedal down; it will eventually settle with the wings far from level but it will fly the heading. And in NAV mode it will track whatever the NAV source is.
However some or all autopilots will disconnect when the roll angle exceeds a certain value. This can happen in turbulence, and possibly happened in the DA42 loss of control case.
I am not aware of a light GA autopilot which does rudder trim, and very few have a yaw damper.
This all comes down to one’s belief in certification over one’s personal experience.
It’s rather like warnings on motorways. If you tell people of fog or debris too often when it doesn’t exist, they stop taking any notice.
Similarly, we have the endless debate about demonstrated crosswind component vs the actual capability of the aircraft, with lots of assertions that limits are as low as they are because there was never a stronger wind encountered during certification, or the test pilot underestimated the capabilities of average pilots.
Another one is POH limitations on LoP operations, which, I think that most experienced pilots now recognise as being Marketing led and actually contrary to the best way to operate engines, and anyway now superseded by better engine instrumentation.
A lot of us have flown MEPs OEI (whether simulated or real) on autopilots with not the slightest problem. Many of us consider it safer, overall, than hand flying while dealing with the emergency itself, diversion, fuel planning and management and, in all likelihood, distressed passengers.
So, the difficulty is that the POH/AFM has lost our total credence, in the face of our own collective experience.
Maybe if we knew why autopilots are proscribed OEI, we might be able to discuss it. But while we suspect that it may be the result of misplaced risk assessment (in other words, if they allow it to be used and there is an accident, it’s their fault, but if they disallow it, it’s the pilot’s fault), or lack of certification resource or opportunity or whatever, we are likely to go with our own experience.
This has been Donne in another thread already.
From experience, in cruise, the 42 handles really well asymmetry. When I had a slow near total loss of power on an engine, the autopilot kept the plane flying perfectly. There were very little indications apart speed of what had happened.
Peter wrote:
I am amazed at this restriction. It defeats the point of an autopilot: it is to free your hands and brain when dealing with an emergency. I also don’t get why this is a real limitation, because surely a twin in OEI flies OK at a reasonable speed?
Nothing to be amazed about. OEI can be controlled exclusively with
1. Roll control (aileron)
2. Yaw Control (Rudder)
3. or any combination of the above
The limitations are very different, the 1st is not even considered in terms of certification limits. i.e. no Vmca considerations or beta slidelip angle tests
This is something that a human can be taught todo very reliably, because he or she has the necessary sensors and brains. But how would a simple GA autopilot make such a determination?
With extra human help the autopilot can be made to work. i.e. rudder trim
On AP, does it make much difference in heading mode vs wing level mode?
The former has less flying tolerances, so probably enough for OEI
From here
The restriction may be due to the A/P not being certified in this condition, which in turn may be due to the A/P leading to a loss of control (probably insidious).
Most puddle jumper A/Ps are two axis, so no rudder input (absent a yaw damper which will not be certified for OEI). Trying to control yaw with roll and pitch (remember 2 axis), may and will result in a fin stall due to excessive Beta sideslip at speeds well above Vmc. The fin stall will result in a nice crisp departure of controlled flight, usually to inverted nose down.
Would an airline or commercial operation ignore an AFM/POH restriction just because on the few times the operator ignored the restriction no harmful consequences resulted?
Single crew MEP flying requires currency, the A/P is not designed to deal with an engine failure/asymmetric conditions.
In an attempt to better understand the certification requirements for autopilots I found this:
https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_23-17C.pdf local copy
The section on autopilots starts at page 250 and runs for about 10 pages. It is a recent document, but the autopilot section is “essentially equivalent” to the previous guidance from 1965! My reading of it suggests that all phases of flight and performance expected of a part 23 airplane, needs to satisfied, unless a limitation is placed on the autopilot.
My guess is then that the manufacture/STC holder, in many cases has simply taken the approach of prohibiting OEI flight with the A/P, using the limitations section of the POH, rather than open a can of worms regarding testing and liability.
In contrast an acceptable means of compliance for part 25 flight guidance systems is over 100 pages… https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_25_1329-1C.pdf local copy
