Using the VPN service makes your internet traffic appear from outside the Cox network. This is no different than if you were traveling abroad overseas (depending on where the VPN service connection is established) and tried to connect to Cox email. As mentioned prior by darius, Cox blacklists US and foreign IP addresses to eliminate email spam and abuse. If you plan to be connected to the VPN service constantly, then you can try contacting Cox to have your device and email account pre-authorized to access Cox email when outside the Cox network.
Do you know this works, or are you just suggesting giving this a try?
The last time I asked Cox about the problem, the Tier 1 support person(s) were completely unhelpful. (I.e., they were ignorant about the issue and just wasted my time.) Apparently, VPN is not part of Cox's training.