Earlier quoted context omitted.
Did the backup drive perhaps become unplugged or fail to unmount cleanly? I've managed to do that to an external hard drive under Linux and had the drive labelled as read-only subsequently. Just wondering aloud...
There is a mounting problem with OS sometimes, too. I don't remember all the occasions, but I am very careful with ejecting the disk (at the moment OS X forces me to shutdown to "eject"). Still, I'd understand if the last backup would be broken that way, but why the whole disk? A backup shouldn't be that brittle.
My understanding is that the kernel labels the device (recognised through its UUID) as 'read only' thereafter. And it is the whole device (i.e. /dev/sdb or whatever) that is labelled.
Your symptoms just struck me as very similar. I can't offer any way forward alas.