Thanks for your input and sorry for my late reply. After the first comments I gave up to find help here. However, already the first leads helped a lot.
So the solution was:
WiFi.persistent(false);
We had to do a lot of testing to validate it and since then the error is gone.
@schufti: You were absolutely right. Thank you.
I do not want to join the commercial thing discussion. Everybody must know for themselves. Just a few sentences about my background. We are a small startup with <10 people. We paid a company money to make our firmware, they included the "WiFi.persistent(false);" bug and were not able to fix it while we were loosing our (few) first customers. That is when I in despair headed here.
I think, we do not have the skills in our team to provide input to the community. If we at one point find a skilled firmware developer I will be happy to share our findings here.
Thank you and best wishes
Peter