In fact, it appears that the programming of the EEPROM *was* failing, and it was my own fault.

The project that the XS40 is being used with involves a software program that uses a parallel-port execution key for copy protection. I can program the XS40 through it normally without an error, which is why it hadn't jumped out at me right away, but apparently something in the EEPROM programming process is different enough to allow the key to cause a problem. Taking the key out of the path between the computer and the XS40 allowed the programming to work, and my XS40 now powers up and configures itself correctly from the EEPROM.