In 2012, less than one percent of the background checks run were denied. A total of 432,387 firearm transactions were conducted in Virginia last year (note that a single background check does not necessarily correlate to individual firearm sales as an individual could be purchasing two shotguns at one time and only one background check would need to be conducted). In 2011, the total was right at 1%. And not all of those denials were necessarily convicted felons or other prohibited persons attempting to purchase a firearm. Some denials were individuals trying to purchase more than one handgun in a 30 day period, which was not legal from 1993 to July of 2012 with limited exceptions.
It should also be noted that of those 3444 denials last year, the Times Dispatch reports only 531 resulted in an arrest. Which begs the question, were some of those denials false positives as Professor John Lott has indicated?