You can enable persistent logging in the LE settings add-on (requires reboot after) and this will allow you to reboot and then share the previous system log with e.g. journalctl -b1 --no-pager | paste but if the Kodi process simply goes unresponsive instead of actually crashing (which will leave traces) there's probably still nothing to see. You can also look at kodi.old.log (boot -1) to see if there are signs of problems there too. Kodi will also record crash logs, but (again) that requires process termination to happen and other problems like resource starvation won't necessarily effect a crash.
You can also update to a current nightly to see if that magically fixes anything. Backup /storage/.kodi to /storage/.kodi-old first to make downgrading possible.