Raspberry Pi 3 loosing wifi - busy status

[Nachteule]

This is good question.

You will nothing find in Kodi log, I suppose you have to install and run a syslog daemon (I'm using rsyslog, but syslog and syslog-ng should be ok also)

Did you already checked if your RPi automatically reconnects to network after rebooting AP?

AFAIR I had issues here few years ago so I wrote script running in background doing this