There have been suspicious incidents of the instant check system being down, resulting in, at minimum, very long delays in purchasing firearms. IIRC, once was shortly after 911. Plus, even though the law required that the records of approved transactions be destroyed after approval, the system was designed to save them for an indefinite time. The current state of that seems to be that they are purged daily. However that's not to say they aren't on the backups for the computer system. The system could have easily been designed such that the data never made it out of RAM, unless the buyer was ineligible, but it wasn't. The Clinton administrating was keeping the records for an indefinite period.
But the principal is the same, requiring government permission to exercise a right.
I can readily believe that there have been implementation problems that are unfair to gun purchasers. Fixing them, and ensuring good-faith implementation, should be a high priority.