Could solve the problem. It was an issue from upgrading to MIUI 8.3. You have to do a full wipe of the phone.
Here the steps to solve the problem:
Backup the data with Option “Backup & Restore” in the MIUI-Settings (under Additional Settings)
Backup with TWRP
Backup all your data (Music, Pictures, Videos…) - they won’t be in the Xiaomi or TWRP Backup
Do a full wipe of system, data… in TWRP
Install the latest weekly build from
xiaomi.eu
Restore from the Xiaomi-Backup
Install DavDroid - and it will work. It even fixed some other issues i had from the upgrades in MIUI
Of course it will be a bit work, but it’s worth anyway. So always make a Backup and a Restore from the Xiaomi-App from time to time…