Thanks for the help.
I've tried all sorts of unplugging and restarting, deleting preferences, reinstalling, but none of that worked. So I downgraded to 0.7.4 and finally, the device was recognized again. I don't know what the deal is.
I checked the device debug info, and the Kindle was indeed recognized by the software, but it simply wouldn't show up in the UI. Oh well. At least I've got it working again.