The question will be do we want a strong Constitution that is not to be changed at every arbitrary change within society or a diluted and weak Constitution that can be changed at the whim of the average lawmaker.
Well, unless a background check is done, how do we know if you (general) have lost that privilege? I work with abused women and families. It's not unusual for an abuser to uproot his family to another state trying to get around the laws that limit an individual with a violent background.
This would be an appropriate use of background checks, but your right to be placed on said list should be done on an individual basis. When we blanket certain groups into laws we weaken our judicial system not strengthen it.