We thought of a formatting problem, so we first reformatted the 500GB disk as an HFS+ volume, and tried again connecting it to the AEBS. Transfers would work both ways from the PC and the Mac through the AEBS. But after connecting the disk directly to the PC and transfering files with TransMac, then plugging the disk back on the AEBS, we would get the same problem with an unmountable share (the problem wouldn't appear after connecting the disk directly to the Mac).
We restarted the base station several times using the AirPort Utility without success. Until, on a hunch, I decided to try unplugging the power plug from the AEBS, and then plugging it back in. After trying the same procedure several times, this appeared to reliably lead to the recognition and mounting of the shared hard disk.
Unfortunately, we didn't have time to test more scenarios (like reformatting the disk as FAT32), but the bottom line is: restarting the AEBS from the AirPort utility doesn't seem enough, so unplugging the power and plugging it back may be more helpful.

