Can you connect the DAP directly to the ISP modem and test NTP services?
My wife is out of the house/office for the next 6 hours, so I've got a bit of time to troubleshoot a couple of network and telephone issues, including this one.
With the DAP connected directly to the DSL modem, the (apparent) NTP Server problem disappears completely. The time is set correctly when using either the URL or the IP address for the D-Link NTP Server. Furthermore, I can ping any URL I like from the DAP in this configuration.
So I'll still convinced that this is a DNS problem, to which the Double NAT configuration of my network MAY be contributing. Keep in mind that, even with the router setup as a NAT, I can still ping any URL from my laptop, when it's connected wirelessly to the DAP, even though I can't do it from the DAP. This tells me that there's a problem with the DAP.
Finally, to answer KE2QR's initial question, I've tried using the IP address (205.171.76.135) for the D-Link NTP Server with the DAP in Repeater Mode, and it does work.
Larry ....