This morning the hosting provider closed the ticket. The cause of the problem was a "malfunctioning Hyper-V pool".
As of now, our log analysis just showed up a general "Kernel-Power" error, as you get on rebooting/restarting a system without shutting it down properly before.
Yesterday, we migrated all relevant systems to another provider, running CID since yesterday at 2 PM UTC. The old system is up and running, but all relevant services have been deactivated there. We won't use it again for anything CC/CL/CID-related.
Please excuse yesterday's downtime, and don't hesitate to open a support ticket if you encounter any problems.