I think, the autopilot problem is a typical controlling/automation problem.
In simple: the system that had to be controlled (now, the aircraft) have always many parameters about responding an effect that moves it out from the stable state. The controller have principles, how to control the system, how much effect and when should it apply on the system, to keep in a stable state. These two functions have some common parts. In a good situation, the controller will keep the system in a stable state for every kind of outer effects. In a bad situation, the controller cannot follows the outer effects and will move the system into an unstable state, which means a typical oscillation of the system.
Lets turn it into aviation language: the aircraft have many aerodynamical parameters, like center of gravity, weight, different locations of loads, drag, lifting force, angle of attack... many parameters. The controller: autopilot, have some programmed principles, that how much vertical trim should it apply to keep the plane in the given descending/climbing rate. If you change the system -modifying the center of gravity, aircraft weight, loads...- without fine tuning also the controller, you will probably got an unstable working system, so the autopilot will not be able to keep the plane in a stable climbing/descending rate.
We are in a bad situation, because we can easily change the aircraft parameters, as these are all stored in the aircraft.cfg file, but we cannot change the autopilot response, because it is stored in the aircraft.air file, which is not perfectly discovered.
