Ok, thanks for the heads up.
I had a read on the php documentation and now I am quite overwhelmed and scared to break things on my server ;D
For example, I am tempted to enable session.save_path. However, I have no idea about the side effects of disabled garbage collection and having to deal with it via a cron job.
Since my session was never ended after only 24 minutes in the past, I will first try how it works without without modifications to php.ini.
In case, I run into trouble, I will report back.