Hi tommot,
Your messages are stored indefinitely as long as you always sign in to your account before 270 days straight of account inactivity. Account Inactivity resets your account (which also deletes your messages).
A good workaround to storing those messages is to use an e-mail client and then move the messages to a separate storage device (A CD, USB storage device, or Cloud Storage) that you can periodically back-up.
Thanks