I don't know your network, and especially if using VLANs, but can you put the problem AP on the same switch as your ZD, with similar port settings regarding VLANs?
If you follow our defaults, your ZD management VLAN should be untagged (typically VLAN 1), and there needs to be a DHCP server/Def-gw on that LAN.
Power cycle your AP when setup on the switch, and watch your Monitor/APs page to see if you see that AP activity.
You can also preset your Diagnostics/Debug for your AP MAC address, to help focus on it's activity after being rebooted on the ZD LAN.