Wow what a terrible idea, I too would like the option to use my authenticator every time. GIVE ME THIS OPTION NOW!
I want it to ask me EVERY time because if it doesn't ask, I will never have any warning if my account had been hacked and someone removed the authenticator! Having it ASK for my authenticator code, is my only assurance that the authenticator is actually still attached to my account.
I have watched a security expert in a coffee shop with wifi trick both the shop's router and a customers laptop so that each of those devices thought his laptop was the other device so all her traffic was detoured through his laptop! It was amazing, and scary, to watch. We could see all the chat text, and web pages she was doing, and everything she was downloading, as though he was sitting at her PC. Both MAC ID's and IP addresses can be faked.
I want my authenticator code to always be asked for.
Until they fix this, if you log in to your game and it doesn't ask for your authenticator, you can log into the blizzard.com site and go to manage your account and remove then re-add the authenticator and it will begin asking for your code again at your game log in (for a while, at least.)