It´s getting worse!
I tried to connect using WPS, and it seemed to work, at first. It took ages to assign an ip-address, but finally it got one. Strangely though, it was the same address as my first pi had, which is running for months without problems (I had two different devices with different MAC-addresses with the same IP-address in the list ?!?).
I could access a web-frontend, I think it was the second ones, according to the version-number.
After disconnecting the new pi though, I could not access my first pi anymore, even a restart did not help.
Is it possible that there is a conflict between the two pi´s?