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Disregard 10.6 and 10.7. The rules still apply.
For troubleshooting on this, take a look at this article:
Troubleshooting printer issues in OS X Lion and Mac OS X v10.6
Hope this helps,
Thanks for your answer.
Installing and reinstalling - I tried that several times.
I did not try the software from the page that is referred to, because in the meantime someon suggested I should turn of the powersaving mode from my router. I did that and it seems to work. Since a day I can repetedly print and not only once.
I hope it stays that way.