At what point does one need to replace a chain ring on a mountain bike?
While replacing any part comes down to when you want/can do it, you should replace any damaged part immediately. That's true whether you experience symptoms of failure or not.

Missing teeth on a chainring may not seem like a big deal until another one breaks off, causes chain slip or a dropped chain that sends you over the bars and into a tree or rock. Suddenly a missing tooth seems like a big deal.

As a side note, you should probably invest in a bashguard/ring if your knocking teeth off your chainrings!