Yeah that's true, thinking about it further a way to solve this could be allowing infinite sessions with the initial passcode being sent to you via SMS.
This way you wouldn't need to remember a different passcode each month and the login attempt issue wouldn't exist because passcodes are generated when you need to login.
Why would I want to remember a different passcode every month?
If after two failed login attempts, I must respond to an SMS before I log in, it's really easy to DOS.
Users will be confused by this new scheme. Stick with what has already been vetted in the industry.