AC doesn't stay on course with AP

I'm sure there is a simple answer to this (probably adjusting the nut behind the joystick); but having read the tutorials to no avail, here I am. For years I've enjoyed mostly low level VFR flights but recently tried some much longer trips and find the aircraft does not stay on course when left on AP.
For example, on a recent flight from London to Tokyo I did everything manually for a couple of hours, over eastern Europe I set the course on the AP and went to bed; the next morning, while the AP and GPS said I was still on course, in reality I was over 300nm north of Tokyo. Flight analysis showed I had flown in a large arc rather than a straight line.
This is not endemic to one AC or one geographic area, I assume this has always occurred but wasn't particularly noticeable due to the comparatively short flights I normally take. Since I have neither the time nor the inclination to sit at my computer for more than a couple of hours, how do I keep the aircraft on course during those long flights?
For example, on a recent flight from London to Tokyo I did everything manually for a couple of hours, over eastern Europe I set the course on the AP and went to bed; the next morning, while the AP and GPS said I was still on course, in reality I was over 300nm north of Tokyo. Flight analysis showed I had flown in a large arc rather than a straight line.
This is not endemic to one AC or one geographic area, I assume this has always occurred but wasn't particularly noticeable due to the comparatively short flights I normally take. Since I have neither the time nor the inclination to sit at my computer for more than a couple of hours, how do I keep the aircraft on course during those long flights?