Retrospective logging of this issue: Carmenta restarted itself unexpectedly a couple of hours ago, but I didn't get any SMS alerting about it while I was sleeping due to what seems to be a bug with Pingdom. I've raised the issue with them and will hopefully have it cleared up soon.
Thankfully Carmenta got itself back up and running with some help from monit and Chef. If you're still seeing any issues, do get in touch.