Losing steps on one axis need not necessarily be caused by the common issues like a loose pulley, poor belt tension or an overheated driver ... 
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Hold on for a sec now...... is that a cracked stepper shaft ?????
Jan
Yepp, it is sheared off (is this the right word? in German "abgeschert").
O.k. the printer has around 7000 operating hours ...
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Yes, right word.... on the surface, do you see any signs of corrosion which could indicate a pre existing crack from manufacturing or transport damage ? I can NOT imagine a 3D printer having so much fore exerted to shear of a shaft that size, the stepper itself would neither have the drive torque nor the holding torque to do such damage.
Jan
Regarding the force or torque I go absolutely confirm with you.
The only thing I can imagine is a little crack during production that became wider and wider with the time.
On the rotor side the shaft has a 6.5mm diameter while the shaft itself has 5mm and exactly at this point where the diameter changes it's sheared off.
Until the moment I noticed the reason for this error I tought I have already seen everything what can happen in 3D-printing 
Sounds like a milling error to me.
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That's crazy! What lead you to determine this was the problem? The motor just wasn't turning?
First symptom was the printbed didn't move as it should - in hindsight crazy, but it still moved sometime a bit.
First tought: a loose pulley - nope.
Removed the belt and the pulley and spin the axle by hand - but most time of a turn - was missing the normal resistance you feel when you spin a steppers axle.
So I decided to open the stepper and have a closer look ...