Yes, clients get their DNS settings from the router over DHCP.
The router's DNS config for that wireless subnet is 10.203.2.1, which is also that subnet's default-gateway/router.
The router itself has a config line of ip name-server listing 2 internal DNS servers and 8.8.8.8
The AP is setup in Dashboard with the internal DNS first, and 8.8.8.8 second.
I am able to ping the internal DNS from the AP in Dashboard, and name resolution does appear to be taking place, but I still get a flurry of those errors throughout the day.
I really appreciate the help on figuring this out.