I just wanted to add my findings in case somebody else is looking for a solution to a similar problem.
It turned out that we have a second jenkins job running on the same machine, mostly unrelated to
the first job that was getting killed. The second job wants to start a process which can only work
if the process isn't already running. Therefore it is looking for processes with a certain name and kills
them if they exist. This pattern now unfortunately also matched a process of the first job and killed
it, assuming it was his own still running process. And as this didn't have anything to do with jenkins
it also didn't show up in the logs.
So it wasn't a jenkins error or resource problem but simply human error.
Thanks for any help and sorry for the noise.