When using Domain Mapping with eNom reseller program it’s necessary to whitelist IP at eNome’s system, otherwise, it will not allow the plugin to connect to API.
There is a message in the plugin during the eNom credentials configuration but there’s no mention of it in the plugin usage docs here: https://premium.wpmudev.org/project/domain-mapping/#product-usage
Also, the information in the plugin is not complete. In some cases, it might be a different IP than the one that your site uses or more than one IP. For example, for some HostGator plans you would need to whitelist both webserver IP (IP used by your site) and host IP (which you, in this case, need to find based on hostname taken from cPanel – by nslookup, tracert or any other method that returns IP of the host).
This might also be a case of setups with e.g. dedicated IPs on shared hosts etc.
Please add this information to both usage guide and in the plugin.