looks like Hardware Version A4 has problem. This shouldn't be this hard. 
Did you accomplish it?
If not, then do the following:
1. Go to Setup - Network Settings and UNCHECK Enable DNS Relay, Save Settings but do not reboot.
2. Go to Status - Device Info and write down the IP Addresses under "WAN" for
Primary DNS Server and
Secondary DNS Server.
3. Go to Setup - Internet - Manual Internet Connection Setup and input the Primary DNS Server and Secondary DNS Server noted in the earlier step, Save Settings and reboot.
4. Restart your network devices so that they will obtain new DHCP leases.
Note: If any of your devices do not get their IP address assignment from the DIR-655, they will need to be manually configured to use the IP addresses you recorded in step 2 for DNS.
If this helps, it's because your network devices are directly using the DNS server addresses now instead of relaying queries through the
buggy "DNS Relay" feature in the DIR-655. Steps 2 and 3 are necessary because of
another bug where the
reboot sequence timing might or might not result in DHCP clients not receiving any addresses at all for DNS. Step 4 is often not necessary, but some network devices may not renew leases and get these changes if they fail to detect that the router has momentarily gone offline.