I have no idea why the NIST servers don't respond to NTP requests, but if you use an IP from the ntp.org pool the EAP will set the time correctly.

Just lookup an IP for 0.pool.ntp.org or for 0.cc.pool.ntp.org (where cc is your ISO country code, for example ' de') and set this IP on the EAP.

Note: hard-coding the IP address of a NTP server is considered bad practice, because it prevents balancing the load on the servers in the pool. Keep in mind that this services are brought to you by volunteers and they expect you to use domain names rather than IP addresses. So please use ntp.org IPs for tests only, not for production use.

If you need an IP for production use, you could set up a local NTP service on your LAN's router (or any server) using official domain names for the NTP server pool and have it delegate NTP services downstream, so you can use the LAN IP of this NTP service on the EAPs.

Please also file a bug-report to your TP-Link support as I have already. This might help to raise the priority of this bug in TP-Link's bug tracking system. :)

I hope TP-Link will fix this bug soon - it's just a bug in the web GUI's java script doing input validation, not in the NTP-related parts of the firmware, so it's not difficult to fix.