Ok, now I found out something interesting.
After one byte is sent and the ISR is called, the 'Acknowledge received' bit in the IBSR is not set. But after the ISR is completed, then, at some point, the 'Acknowledge received' bit is set. I have no idea, why the bit would be set that late.
When I try my other IIC device (which works with my code), the bit is set when the ISR is called (as expected).
Bastian