Thanks for the quick response, jlightner.
I did some experimenting, and it had several different behaviors. Usually the first time after boot, it would automount and I could do some stuff (such as reading or writing files) for a very limited time, then the device would dissapear. It's not just not mounted anymore: it's not in /dev/. If I unplug it and plug it back in, it doesn't show up again until I reboot. When working in recovery mode, it's the same behavior (except for the automounting - I mount it manually), and I get messages that are something like "Assuming write through" and "Logic error block N".
I think what I will try next is to reformat a good usb stick, then reboot and dd the good stick onto the bad stick.