Winston-Salem native Childress, the longtime car owner for Dale Earnhardt, resigned on Monday.
Childress, who was an NRA board vice president, is the fifth leader to depart recently, the stations reported.
In his letter, Childress cited business reasons for his departure.
"Since proudly agreeing to serve on the NRA Board, I have supported the organization and its important mission to preserve and protect our Constitutional rights," he wrote, in the letter obtained by CNN. "But when, as now, I am no longer able to be fully engaged in any commitment I have made, it becomes time for me to step down."
Childress will continue to support many hunting and conservation initiatives "that are near and dear to me," he wrote, and "continue my work to defend our Second Amendment however possible, which I defend with all my heart."