Oops, confused HBO Go with HBO Now.
When you change the password, and enter the new password into the 3rd device, does it disconnect the other two devices? The situation would appear to be there is some 4th devices that is connected with your credentials, and since the limit is 3, it disconnects one when you try to connect YOUR 3rd device.
Can anyone from Cox confirm if HBO Now applies to secondary Cox usernames? I thought it was admin only, but maybe if it's not, someone is using one of your secondary usernames to access. If you don't have many usernames, might not hurt to change the passwords to those too. I just wish Cox had some way to check who/what is logging into your Cox account and from what IP like they do for gmail. I don't even think Cox employees can see that, Tier 1 anyway.