The source of the problem was that the plastic body of the screw threads difficultly into the thread. The feeling is comparable to those metal bolts with rubber seal to prevent vibration.
Consequently, when I was screwing the bolt in, there was no increase in the feedback torque - it was moderately difficult to screw the bolt in, up until the head broke off.
So, firstly I tried to burn a slot in the body of the screw with a heated screwdriver. I got it several millimeters deep, but when I attempted to turn, half of the screw broke off.
Next I tried drilling with a dremmel. The bolt is in the bottom of the front triangle, so even though I used a flexible arm (like the ones at the dentist's), I was unable to attack the screw co-axially and the drill bit constantly hit against the aluminum frame.
Next I tried a soldering iron. Bought a cheap, thin-nose, 30W iron and managed to remove a lot of material. This was the most successful method so far ... almost.
Having done everything possible, I inserted a steel screw and tried to chase the thread with it. To my disappointment, it didn't work. The "nipple" at the frame began rotating, with respect to the frame. The bolt become stuck within the "nipple". Now I need to go to a LBS and ask if they could replace the thing.
Bottom line: don't use plastic screws: they are evil. If you must, use a short-arm wrench e.g. 10 centimetres.