I'm sure all the relevant data is recorded in the event log, which is how it should be done. In fact, I do believe that's what the error message says in smaller font.
> Where is it recorded when the OS kernel loses access to persistent storage?
When your drive/chipset dies and you reboot, you'll get an error saying that no bootable drive is found. It'll be pretty obvious what happened at that point.
KeBugCheckEx(), the method that displays a blue screen, dumps memory to the paging file (which is contiguous and fixed, so it doesn't need the FS driver). When a dump is about to be made, it hashes all of the pieces of the pager and the disk driver necessary to do the dump, and ensures that they aren't corrupted, then dumps. On reboot, the boot manager notices that the system died messily, and copies the paging file to a crash dump.
Now you know more than you ever wanted to about blue screens. :)