Each re-auth requires a fresh code from the app.
I access google apps via Safari because Apple's mail app has no real search function. Since the codes expire in 60 seconds, I'm on a timer for writing it down, launching safari, refreshing to get the "login failed" screen, entering in my username and password without errors and then entering in my code. Totally doable, but irritating. Imagine you're in a hurry, and checking your email as you walk down the street. You open your client and instead of your email you get an error. The error doesn't tell you what's wrong, it just says there's a problem with your login. Hopefully you remember that 30 days ago you reset your token, and that's the problem. Now you can pause everything else, and setup your email.
Don't have a pen to write down your code while you switch apps? How's your memory?
I totally get that good security involves expiration dates, but I want things that "just work", not that "usually work".
In principle it's a great idea, and if I could choose how often it expires I'd be a happy camper.
</rant>