St. Thomas US Virgin Islands appears not to be paying their refunds from last year. Do I have to claim it as income when I have never received it? Can I somehow claim it as a loss since it appears it will never be paid?
No, you will not report any USVI-source refund as income on your US federal income tax return. Additionally, you will not be able to claim a loss on your US income tax return for any missing tax refund payment.
You can contact the Virgin Islands Bureau of Internal Revenue related to your missing USVI tax refund.
You will want to have a copy of your 2015 Form 1040 (with all attachments, forms, and schedules, including Form 8689) that you send to the USVI when contacting the VI Bureau of Internal Revenue.
Here is the link to the Virgin Islands Bureau of Internal Revenue: http://www.vibir.gov/