Good point! 
The piston was indeed not moving at all (yes, hard time) and the plastic was (still is) cracked. I was afraid if the plastic would fall apart during removal of the piston. That's why I had marked the segments with numbers before removal. But the plastic remains still in position although it seems that it will fall apart in the next second. I sanded the plastic's circumference a little and lubricated it and the cylinder wall with a thin film of silicone grease. Now the air brake is functioning well again and gives the escapement smooth movements.