When submitting a 4473 to NICs, you never get a reason. The buyer has to call appeal to NICS directly.
Suggest you get the forms direct from ATF. Especially since they send them out for free. https://www.atf.gov/distribution-center-order-form
If you get a *reasonable* examiner, they might work with you to complete the missing information on the FPCS. Just don't count on it.
When you get...
I would think that if you download your application, the box for "Disapproved" would state the reason since that is in parenthesis next to the checkbox. Have you tried using the "Ask the Experts" on the eforms page?