Is the Blaze stool connected to your Fitbit account?
Impairing the Blaze should not disconnect it from your account, and simply opening the app up should pair it up. This pairing of the Blaze can only be done through the app.
I have switched phone's 3 times, done 2 factory resets, and never had to do more then log into my account through the app to get the Fitbit to pair up and sync.