I had Avast's security thing installed on it, so I figured it must be something to do with that, where it claims to prevent flashing on a stolen handset among other things. I uninstalled all the Avast stuff and it looked as if the phone happily booted normally every time again.
Sadly, not so. It's happened again a few times since, booting into bootloader and needing about three "reboot" cycles to boot properly into the OS.
It seems to happen only after the phone has been powered off for a long time - say in excess of several hours. If I simply use Android's "Restart" option, or power down fully and restart it again, it will reliably boot into OS normally.
In short: If left powered down for more than a few hours, phone requires about 4 uses of "Reboot" option in the bootloader before finally properly starting into the OS.
This may or may not be of use, but it's some field data to be aware of.