As you mentioned, some APs connect briefly. Eliminating the possibility of intermittent network connection, every once in awhile, the APs try to download the configuration from ZD over FTP. If there is a firewall in between the APs and the ZD that is blocking FTP access to ZD, then you will witness this exact behavior. Check the reason for disconnect.
To further answer, if were to manually configure an AP, the problem will return when it will connect to ZD.