ANSWER: As long as you are logging in to your WP StageCoach staging site often (i.e. every few days or so) then it should remain active. However, after around 3 weeks of no logging in, your staging site will be automatically deleted by WP StageCoach in order to clear up space on their system and for security/privacy reasons.
If you have a very long-term project that requires a long term staging environment we recommend not relying on WP StageCoach and instead setting up a temporary site somewhere on a cheap hosting company, i.e. Bluehost etc. The WP StageCoach system is really aimed at short-term testing of new features to make sure that there is no serious conflict or issue on your site before launching those features live on your production site, and is not meant as a long-term hosting solution.