What can cause headset bearings to become loose quickly?
A few months ago, I finally found the most likely reason for my problem: Instead of a star nut, this bike uses an expander plug under the top cap. This plug extends about 4mm above the end of the steerer tube, like this:

######### 
|#######|
|#######|
|#######|


Where the # represent the plug, and the | is the steerer tube. I had the stem at the topmost position, and I suspect that it not only gripped the tube, but also the compression plug. Which in turn was loosened by vibration and the stem moved upwards with it, loosening the bearings.

I have since moved a spacer above the stem so that it does not touch the plug; this seems to have fixed the problem. The lower handlebar position is fine with me, and my problem hat not re-occurred for the last months despite riding some rough-ish trails.