Recently I have experienced that, while in level flight, the autopilot disconnects and the joystick goes haywild, thrashing wildly up/down (not turning though). It has been behaving perfectly before, and I haven't changed any settings, but all of a sudden this phenomenon started.Anyone has an idea what has happened?

Sounds like your joystick is having issues. If you have the purchased version of FSUIPC check the axis values and see if they are jumping around.