I found a work-around for this issue.  Instead of entering the amount paid with the original return into the 1040-X worksheet, I entered it into the Tax Payments screen (with the date my client paid the original tax with his return).  If it is entered this way, the "Direct Deposit" information should automatically populate for you on the amended return.

Update: I noticed when I view the 1040-X, the direct deposit information shows on the worksheet, but it does not show when I print the 1040-X, so I am not sure if my work-around will actually fix the issue.