Running diskutil list from the command line confirmed that there was no partition map on the bad disk. Running pdisk from the command line, then issuing an L further confirmed the lack of a partition map.
Because this is a mirror, it was a safe assumption that the map on this disk should be the same as on the other disk in the mirror. Using pdisk, I initialized the partition map on the bad disk (by typing i), then created each entry in the partition exactly as on the other disk. After writing the updated partition map, the disk partition magically reappeared in Disk Utility, and the RAID came back up. Data was still there and everything was still accessible.
I'm not sure how the partition map got corrupted, but if you've got no hope of recovering your stripe, give this a try.

