I agree 100%. Forfeiture of rights (the idea that people give up their rights by performing certain actions) is a very important concept for any moral or legal system. Without it, felons would still have their right to liberty and would be free to leave prison and go wherever they want.
Thankfully, most states require extensive background checks for anyone who wants to buy a gun. I would argue that such processes should be enforced more regularly, before any new legislation is made on the matter.
Another idea that I like is the idea of "gun ownership restraining orders". Basically, it would allow people to appeal to judges to have a friend or family member of theirs temporarily barred from being able to buy, keep, or carry guns. This would of course require a great deal of evidence and warrant to be presented before the order is given, and would have to allow the accused a chance to offer a defense in court. Properly balanced, though, a process such as this could significantly decrease the amount of suicides (a statistically significant amount of gun deaths), and murders between friends and family (a large portion of murders in general).