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I have 3 Rokus in my house and HBO Go is installed on all 3 of them. Starting with the recent "new" app upgrade I've ran into an issue. If I activate only 2 of them there's no problem but if I activate the 3rd one the first two get logged out. Then if I reactivate the 1st two the 3rd one gets logged out. And I'm not talking simultaneous streams, I'm talking just being logged in to see the watch list, etc. I don't have this issue with any other providers so is Cox limiting how many devices can be used?
I would suggest changing your HBO Go password and trying again. HBO GO only works on 3 devices I think, so if someone else is using the password for a 4th device, even if not on your network, it may be causing a problem. Also make sure your not using a sub-account, and using the admin(first) username/password on the Cox account.