Thanks for the logs!
Unfortunately, I don’t have any idea what the problem could be.
It is expected that DAVDroid syncs every 24 hours and on local change
It seems DAVDroid has troubles determining whether there is an Internet connection and is not responsive to sync now.
What I discovered is that if you enter the Manage accounts menu and immediately exit, DAVDroid starts the sync.
DAVdroid does not determine whether there is an Internet connection. That’s all up to Android’s sync logic, which calls DAVdroid.
Did you have a look at FAQ: Why is synchronisation not triggered as set it in sync interval settings? Did you disable app standby for DAVdroid? Which Android version do you have? Which device do you have? Is there any additional information which could be useful for debugging?
Also, please provide steps to reproduce and debug info.