We're running into an issue where the database can't be connected to. It appears that the auto-vacuum is timing out and then that prevents new connections from happening. This assumption is based on these logs showing up in the logs:
WARNING: worker took too long to start; canceled
The log appears about every 5 minutes and eventually nothing can connect to it and it has to be rebooted.
As Julien suggested, this sounds like another victim, not the cause. Is there anything else in the log files?
That's the only thing in the logs for the 12-24 hours before the database becomes inaccessible.
To follow up on this, this was the symptom and not the cause. The auto-vacuum was failing to start because of a bug and not the cause of the problem.