Was the refund going by direct deposit to a checking account at your bank or to a prepaid debit card? Have you checked with the bank or card company to see if an attempted deposit was made and refused? If the direct deposit was refused, it would go back to the KY state DOR, who would issue you a check by mail.
Here's how you can contact the Kentucky Dept. of Revenue so that they can troubleshoot with you:
https://ttlc.intuit.com/replies/3302452
