I was wondering whether readsb can be set up so it logs every last known position of a tracked aircraft to a json file.
I have found the history_XXXX.json and latest_XXXX.json files but they are not persistent.
Is there a possibility to create a persistent database that allows me to search for registrations etc.?
Reply to myself 
I have found a good solution for me:
→ VirtualRadarServer headless on one of my feeders with the DatabaseWriter, DatabaseEditor and WebAdmin Plugin.
I can combine all the feeds into one and have the database saved in a format that works out for me.
That’s the “big” solution.
If you only want to build a database where your daily flight movements are logged, a simply python script is doing the job.
I am using this one, slightly adjusted to my needs and it works perfect:
http://cactusprojects.com/logging-dump1090-fa-to-local-database/
All information are going into a SQLite DB which then can be processed by any tool which is able to connect it.
With a little programming skills it can be adapted to a MySQL version.
You should not have it running on a Raspberry (also not VRS) as the write attempts might damage your SD card sooner or later.
I have a virtual instance for it running on my Proxmox server.
Or you can add a small SSD drive to the Raspberry.