The only reasons you'd be asked for an authenticator code every time you log in would be:

  1. You have the option enabled, in your account, to do so
  2. You are using multiple Battle.Net accounts

You already said that #1 isn't the case, so I assume it's #2. If you're using ISBoxer, then setup a Virtual File. If you're not using ISBoxer, then either ask Blizzard to merge your accounts under one BNet, or drop the authenticator from some of them.

However, there's a third, bonus reason, and that's that your physical hardware or IP is changing, which I doubt you're doing between launching each game client, so it's not even worth mentioning. Unless, of course, you're running a multiple computer setup, in which case it is worth mentioning, which is why I mentioned it.